Grade 10 / Probabilities 51 exercises (100% corrected)

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AsAsAsAsRRRRDDDDVVVV10101010999988887777♥♦♠♣ 123456123456 ChingQuizz : 6 exercises available for Quizz assessment : 1. Equiprobability E.5905 A game consists of randomly drawing from a deck of 32 cards. The following events are considered : A : ˇ The card is a figure ı ; B : ˇ The card is rouge ı ; C : ˇ The card has a value between 8 and 10 ı 1 What is the probability of the event C ? 12 32 14 32 16 32 18 32 2 What is the probability of the event A ∪ B ? 16 32 17 32 22 32 23 32 3 What is the probability of the event B ∩ C ? 3 32 4 32 10 32 12 32 2. Two-outcome equiprobability E.5178 For each question, compare, if pos-sible, the probability of the two events presented : 1 By rolling two six-sided dice simultaneously : A : ˇ The sum of the dice is 2 ı ; B : ˇ The sum of the dice is 3 ı. 2 Two six-sided dice are thrown successively: C : ˇ We get 1 , then 1 ı ; D : ˇ We get 1 , then 2 ı. 3 Consider a class of 24 students : E : ˇ The student chosen is a boy and practices foot-ball ı ; F : ˇ Among boys, the student chooses practices foot-ball ı. E.4511 1 Consider the random experiment of throwing two six-sided dice and summing the value of each dice. The following events are considered : Event A: ˇ we get 8 ı. Event B : ˇ we get a value greater than or equal to 6 ı. Event C : ˇ One of the dice has the value 4 and the sum is greater than or equal to 7 ı. a Complete the following table : b Determine the probabilities of the events A , B and C . 2 We change random experiments. We’re still rolling these two dice, but we’re now interested in the value of each of the dice. Determine the probability for the following events : a Event D : ˇ both dice have the same value ı. b Event E : ˇ we get 6 and 4 ı. c Event F: ˇ one of the dice has the value 3 and the other has an even value ı. https://chingmath.fr chapExoCorrec/5905 sacados/5905 AsAsAsAsRRRRDDDDVVVV10101010999988887777♥♦♠♣ chapExoCorrec/5178 sacados/5178 chapExoCorrec/4511 sacados/4511 123456123456
RTC1C2PRT1T2P1P2LucSophie ABM1M2N1N2 E.7276 Sophie and Luc play chess very badly, so they invented the following game: Sophie has a bag containing five white pieces : a queen, a rook, two knights and a pawn. Luke’s bag contains five black pieces : a queen, two rooks, and two pawns. Game principle : Everyone draws a coin from their bag, whoever has the strongest coin wins the game: A queen beats all other pieces. A rook beats a knight or pawn. A knight beats a pawn. Two identical pieces draw. Examples: Sophie draws a queen and Luke a rook: Sophie wins the game. Sophie and Luke both draw a pawn : there is a draw. 1 In the table below, each box corresponds to a possible outcome of the game. Copy this table and complete each box: By a S when Sophie wins. By a L when Luke wins. By a N when the game is tied. 2 Calculate the probabilities of the following events : a A : ˇ the part is nulle ı b B : ˇ Sophie gagne ı c C : ˇ Luc gagne ı 3 Is there, from the point of view of the contents of the bags, one player at an advantage over the other? Justify the answer. E.3111 We have two six-sided dice, num-bered from 1 to 6 , which are thrown simultaneously : 1 We consider the following two events : A : ˇ We get a double 1 ‘’; B : ˇ We obtain a 1 and a 2 ‘’. Justify the values of the following probabilities : P ( A ) = 1 36 ; P ( B ) = 1 18 2 Determine the probabilities of the following events : a C : ˇ The sum of the two digits is equal to 5 ‘’; b D : ˇ The sum of the two digits is greater than or equal to 8 ‘’; c E : ˇ Both digits are odd ‘’. E.2659 Two fair dice are rolled. Determine the probability of each of the following events : 1 Event A : ˇ we get a 6 and a 2 ı ; 2 Event B : ˇ the sum obtained is strictly greater than 8 ı ; 3 Event C : ˇ the two numbers obtained are even ı. E.4514 Consider a mobile whose start is point A and moving on the grid below only by upward and rightward movements : By choosing an exit (shown dotted) , the game stops. 1 How many paths allow the mobile to leave the game board in M 1 ? in M 2 ? By symmetry of the figure and the displacements of the mo-bile, we admit that there are respectively as many paths al-lowing the mobile to exit in N 1 and in N 2 as in M 1 and M 2 : 2 Determine the number of paths allowing the mobile to exit in B . 3 Randomly choosing one of these paths, what is the prob-ability that this path will cause the mobile to exit in B . 3. Equiprobability and choice tree E.3051 An urn contains two black balls and one white ball; each is numbered from 1 to 3 . The game con-sists of drawing two balls successively with delivery: i.e. a first ball is drawn, then returned to the urn before drawing a second ball. Here’s a decision tree based on the drawing of two balls : https://chingmath.fr chapExoCorrec/7276 sacados/7276 Sujet du bac STI Juin 2004 RTC1C2PRT1T2P1P2LucSophie chapExoCorrec/3111 sacados/3111 chapExoCorrec/2659 sacados/2659 chapExoCorrec/4514 sacados/4514 ABM1M2N1N2 chapExoCorrec/3051 sacados/3051
N1N1N1N2N1N2B3N1B3N1N1N2N1N2N2N2B3N2B3N2N1B3N1N2B3N2B3B3B3B3 234561Première roue2341Seconde roue 123546UrneBUrneA Once the two balls have been drawn, consider the two colors obtained and the order in which they were drawn 1 How many elementary events make up this random ex-periment? 2 Determine the probability of the following events : a A : ˇ The first ball drawn is blanche ı. b B : ˇ The two balls drawn are différentes ı colors. c C : ˇ The second ball is a noire ı ball. E.6681 Two wheels are available to obtain numbers : the first wheel is numbered from 1 to 6 , the second wheel is numbered from 1 to 4 : The two wheels are assumed to be perfectly balanced and it is assumed that for each wheel, obtaining a number represents a situation of equiprobability. 1 These two wheels are used to construct an integer con-sisting of two digits : the first wheel will form the tens digit, the second wheel will be used for the units digit. a Construct the choice tree corresponding to this situa-tion. b Consider the following events : A : ˇ the number consists of the same two chiffres ı B : ˇ the units digit is strictly greater than the dizaines ı digit. Determine the probability of the events A and B . 2 We change the rules of the game: we add up the numbers obtained on the two wheels. Does this new experiment represent a situation of equiprobability? Justify your answer. E.11589 Consider the two urns below con-taining balls with numbers written on them : The random experiment consists of drawing a ball at random from urn A , then a ball at random from urn B , and calculat-ing the difference between them. 1 Construct the tree of possibilities for this random exper-iment. 2 What is the probability of obtaining a number strictly greater than 3 ? E.4530 An urn contains four balls bearing the letters A , B , C and D respectively. A participant in the game must draw three balls in turn without returning them to the urn and write down the word formed by its three letters. 1 Construct the choice tree corresponding to this random experiment. 2 Determine the probability of the following events : a A : ˇ The word begins with the letter A and ends with the letter D ı ; b B : ˇ The word contains the letter A and the letter D ı ; c C : ˇ The word contains the sequence AB ı. E.2658 We randomly compose a three-letter word with the letters A , B , C : 1 How many words can be constructed? 2 Determine the probability of each of the events below : a E 1 : ˇ The word begins with the letter C ı ; b E 2 : ˇ Word begins and ends with the letter A ı ; c E 3 : ˇ The word contains exactly twice the letter B ı ; d E 4 : ˇ The word contains only A ı ; e E 5 : ˇ The word is made up of exactly two letters dis-tinctes ı ; 4. Law of probability E.3072 Here is a table showing the proba-bility distribution of a six-sided rigged die : x i 1 2 3 4 5 6 p i 0.15 0.1 0.08 0.17 0.22 0.28 Determine the probability of each of the events below : 1 A : ˇ The number obtained is greater than or equal to 4 ı. 2 B : ˇ The number obtained is pair ı. https://chingmath.fr N1N1N1N2N1N2B3N1B3N1N1N2N1N2N2N2B3N2B3N2N1B3N1N2B3N2B3B3B3B3 chapExoCorrec/6681 sacados/6681 234561Première roue2341Seconde roue chapExoCorrec/11589 sacados/11589 123546UrneBUrneA chapExoCorrec/4530 sacados/4530 chapExoCorrec/2658 sacados/2658 chapExoCorrec/3072 sacados/3072
112233445566BleuRouge E.4531 Here is a table showing the prob-ability distribution obtained by throwing a rigged six-sided die : x i 1 2 3 4 5 6 p i 0.11 0.14 0.1 0.15 0.12 0.38 Determine the probability of each of the events below : 1 A : ˇ The number obtained is strictly less than 4 ı. 2 B : ˇ The number obtained is impair ı. E.4508 An urn contains red, green and blue balls that are indistinguishable from each other to the touch. The random experiment under consideration consists of draw-ing a ball at random from the urn. We don’t know the contents of the urn, but we do know the probability law of this random experiment from the table be-low : x Rouge Vert Bleu P ( x ) 0.3 0.6 0.1 Knowing that the urn contains 120 balls in total, determine the number of balls of each color. E.5187 A random experiment con-sists in rolling two dice, red and blue, with six faces simultaneously and considering the sum ob-tained by these two dice. The dice are assumed to be perfectly balanced. 1 Describe the universe of possible outcomes. 2 a Complete the ta-ble below : a Determine the probability law associated with this random experiment. 5. Property of a probability law E.4790 Consider a loaded six-sided die, part of whose probability dis-tribution is given in the table below : X 1 2 3 4 5 6 P ( X ) 0 ; 14 0 ; 07 0 ; 12 0 ; 1 Furthermore, the probability of rolling an odd number is 0 ; 4 . Justify your approach and determine the missing values in this table. E.6682 Consider a rigged die with 6 faces. The random experiment consists in throwing the die and con-sidering the value of the top face of the die. For k an integer between 1 and 6 , consider the event F k de- fined by ˇ the value obtained is k ı The only information on the die is : The incomplete table of the probability law of this ran-dom experiment : X F 1 F 2 F 3 F 4 F 5 F 6 P X 0.11 0.07 0.2 0.15 The probability of getting an even number is 0.4 . Copy and complete the probability distribution table for this random experiment. The steps of your reasoning must be present on the copy to be assessed. 6. Determine the probability law E.3093 An urn contains 12 white balls, 5 black balls and 8 blue balls, indistinguishable by touch. Con-sider our universe of experience composed of the following three elementary events : A : ˇ The ball drawn is blanche ı B : ˇ The ball drawn is noire ı C : ˇ The ball drawn is bleue ı Complete the table below, to the nearest hundredth, repre-senting the probability distribution of our experiment : X A B C P ( X ) E.4507 An urn contains 20 % red balls, 50 % green balls and the rest blue balls. The balls are indistinguish-able to the touch. The random experiment under consideration consists of draw-ing a ball at random from the urn. Determine the probability distribution of this experiment. https://chingmath.fr chapExoCorrec/4531 sacados/4531 chapExoCorrec/4508 sacados/4508 chapExoCorrec/5187 sacados/5187 112233445566BleuRouge chapExoCorrec/4790 sacados/4790 chapExoCorrec/6682 sacados/6682 chapExoCorrec/3093 sacados/3093 chapExoCorrec/4507 sacados/4507
1234 AB AAB AAB BAB BAB ABAB ABAB ABAB ABAB ABAB ABAB ABAB E.4506 An urn contains four balls numbered from 1 to 4 . The balls are assumed to be indistinguishable to the touch, making each draw equiprobable. The random experiment consists in drawing a first ball, then without putting it back, drawing a second one from the urn. In each experiment, the sum of the two numbers marked on the balls is noted. 1 Construct the choice tree modeling this experiment. 2 What are the possible output values of this experiment. 3 Using a table, specify the probability law P of this ran-dom experiment. E.4509 The faces of a tetrahedral die are denoted with the letters A , B , C and D . This die is assumed to be perfectly balanced. The random experiment consists of rolling the die three times and noting, each time, the letter of the hidden face. Thus, at each exit from the random experiment, a three-letter word is constructed. 1 Write the 64 words that can be obtained in this random experiment. 2 Give the probability of the following events : a E 1 : ˇ The resulting word contains the letter B ı exactly once ; b E 2 : ˇ The word obtained contains exactly twice the letter B ı ; c E 3 : ˇ The word contains the same letter on the first and third place ı. 3 Consider the following game around the previous random experiment : If the three letters obtained are identical then the player wins 5 e . Otherwise and if the first letter and the third letter are identical then the player wins 2 e . Otherwise he wins nothing. We note ˇ X = k ı the event ˇ the player wins k e ı. Com- plete the table below : k 0 2 5 P ( X = k ) E.4554 In a random experiment, the player throws a tetrahedral die whose faces are numbered from 1 to 4 . Next: If the face of the die is even, the player draws a ball from the urn A ; If the face of the die is odd, the player draws a ball from the urn B . Here are the contents of these two urns : The urn A contains one white ball and one black ball. The urn B contains two black balls. 1 Construct a choice tree representing the different outputs of this random experiment. 2 Considering that the outputs of this experiment are equiprobable and that only the color of the ball drawn is considered, describe the probability law assigned to this random experiment. E.4562 A perfectly balanced wheel is divided into 16 equal parts di-vided into four divisions où inscribed with a number on each. The random experiment con-sists of spinning the wheel and recording the number ob-tained when the wheel comes to rest under the arrow 1 Describe the universe of this random experiment. 2 Give the probability law of this random experiment. 7. Operations on events E.5865 Below are representations of the universe Ω of a random ex-periment and two events A and B of Ω . For each of the representations below, shade the requested set. https://chingmath.fr chapExoCorrec/4506 sacados/4506 chapExoCorrec/4509 sacados/4509 chapExoCorrec/4554 sacados/4554 chapExoCorrec/4562 sacados/4562 1234 chapExoCorrec/5865 sacados/5865 AB AAB AAB BAB BAB ABAB ABAB ABAB ABAB ABAB ABAB ABAB
ABaABb ABcABd ABeABf AB ABC ABC ABC ABC ABC ABC E.8151 In the universe Ω of a random ex-periment, consider two events A and B . For each of the events below represented by the hatched part of the diagram, describe this event using the events A and B , their complementary, union and intersection : E.11586 Consider a random experiment where its universe Ω and its elementary events are represented below : For each of the sets below, give the number of elementary events it contains : a A b A ∪ B c A ∪ B d A ∩ B E.8152 In a universe Ω , consider the three events A , B and C shown below. For each question, express the hatched part using the events A , B , C , their complement, union and intersection. 8. Operations and probabilities E.4510 Consider a balanced die whose six faces are numbered from 1 to 6 . Consider the following three events : A : ˇ The number obtained is 5 ı ; B : ˇ The number obtained is strictly greater than 3 ı ; C : ˇ The number obtained is impair ı ; 1 Determine the probability of events A , B , C . 2 Consider the events below : a A ∪ B b B ∩ C c A ∪ B d B ∩ C Describe each of these events, naming the elementary events that make them up, then give their probability. E.4563 A dodecahedral die has 12 identical faces numbered from 1 to 12 . It is assumed that its faces each have the same probability of exit. When a throw is made, the top face of the die is noted. Consider the following events : A : ˇ The number obtained is pair ı B : ˇ The number obtained is greater than or equal to 9 ı C : ˇ The number obtained is strictly less than 6 ı 1 Determine the probabilities of events A , B and C . 2 Give, without,justification, the probabilities of the fol-lowing events : a A ∩ B b A ∩ B c B ∩ C d B ∪ C e B ∩ C f A ∪ C https://chingmath.fr chapExoCorrec/8151 sacados/8151 ABaABb ABcABd ABeABf chapExoCorrec/11586 sacados/11586 AB chapExoCorrec/8152 sacados/8152 ABC ABC ABC ABC ABC ABC chapExoCorrec/4510 sacados/4510 chapExoCorrec/4563 sacados/4563
AB AsAsAsAsRRRRDDDDVVVV10101010999988887777♥♦♠♣ NNNBNBNNNNBNBNNBNNBNB E.11585 Consider a random experiment representing a situation of equiprobability. The diagram below represents the elemen-tary events of the universe Ω as well as the two events A and B . 1 Determine the probability of event A ∩ B ? E.5909 Consider a loaded six-sided die whose probability distribution is given in the table below : x 1 2 3 4 5 6 P ( x ) 0 ; 14 0 ; 07 0 ; 22 0 ; 12 0 ; 1 Consider the following events : B : ˇ The face has a value strictly greater than 2 ı ; C : ˇ The face has a value less than or equal to 5 ı ; What is the probability of event B ∩ C ? 0 ; 42 0 ; 44 0 ; 46 0 ; 48 E.5352 Consider a deck of 52 cards and the following events : A : ˇthe card is colored rougeı ; B : ˇthe card is not a figureı. Determine the following probabilities : a P B b P B ∩ A c P B ∪ A d P B ∩ A E.6683 School management takes stock of students enrolled in half-board : The school has 852 students ; In total, there are 213 students enrolled in the ˇ externe ı scheme ; For girls, 123 girls are enrolled in the ˇ externe ı plan and 312 are on half-board 1 Copy and complete the table below : Garçons Filles Total Externe Demi-pension Total 2 Consider the events : G : ˇ the student is a garçon ı ; E : ˇ the student is enrolled in externe ı. Determine the probability of the following events : a G ∩ E b G ∪ E c G ∪ G E.5906 A game consists of drawing randomly from a deck of 32 cards. Consider the following events : A : ˇ The card is a face card ı ; B : ˇ The card is a heart ı ; C : ˇ The card has a value between 7 and 10 ı Determine the following probabilities : a C b A ∪ B c B ∩ C 9. Operations and choice trees E.3053 An urn contains two black balls and one white ball; the game consists of extracting two balls from the urn without delivery: the first ball drawn will not be returned to the urn. Opposite is a choice tree repre-senting the draws in this game. 1 Taking into account the order in which the balls are drawn, what is the possible number of different draws? 2 Determine the probability of the following events : a A : ˇ The first ball drawn is blanche ı. b B : ˇ The second ball drawn is blanche ı. c C : ˇ The two balls drawn are distinctes ı colors. 3 Give the probabilities of the following events : a A ∩ B b A ∩ C c C https://chingmath.fr chapExoCorrec/11585 sacados/11585 AB chapExoCorrec/5909 sacados/5909 chapExoCorrec/5352 sacados/5352 chapExoCorrec/6683 sacados/6683 chapExoCorrec/5906 sacados/5906 AsAsAsAsRRRRDDDDVVVV10101010999988887777♥♦♠♣ chapExoCorrec/3053 sacados/3053 NNNBNBNNNNBNBNNBNNBNB
NNNNNNNNNNBBNNNNNNNNNNNBBNNBNNNBNNNBBBBNNNNNNNNNNNBBNNNNNNNNNNNBBNNBNNNBNNNBBBBNBNNNBNNNBNBBNBNNNBNNNBNBBNBBNNBBNNBBBBBB AsAsAsAsRRRRDDDDVVVV10101010999988887777♥♦♠♣ AsAsAsAsRRRRDDDDVVVV10101010999988887777♥♦♠♣ AsAsAsAsRRRRDDDDVVVV10101010999988887777♥♦♠♣ E.3052 An urn contains two black balls and one white ball; the game is played with the drawn ball re-turned : i.e., once drawn, the ball is returned to the urn before the next draw. Here’s a decision tree based on the drawing of three balls : 1 Taking into account the order in which the balls are drawn, what is the possible number of different draws? 2 Determine the probability of the following events : a A : ˇ The first ball drawn is blanche ı. b B : ˇ The three balls drawn are the same couleur ı. c C : ˇ At least two balls drawn are the same couleur ı. 3 Give the probabilities of the following events : a A ∩ B b A ∩ C c C 10. Operations and card games E.3049 Consider the 32-card deck shown opposite. The random experiment consists of choosing a card at random from the deck. 1 For each of the events below, deter-mine the number of elementary events making it up : a A : ˇ The card drawn is a carreau ı. b B : ˇ The card drawn is a as ı. c C : ˇ The card drawn is a figure ı. d D : ˇ The card drawn is rouge ı. 2 Determine the cardinal of each of the following events : a A ∩ B b B ∩ C c B ∪ D E.4529 Consider an experiment consisting of ran-domly drawing a card from a deck of 32 cards and the four associated events : A : ˇ the card drawn is a roi ı ; B : ˇ the card drawn is a figure rouge ı ; C : ˇ the card drawn is a coeur ı ; D : ˇ the card drawn is a nombre ı 1 Determine the probability of the four events A , B , C and D . 2 Determine the probability of the following events : a A b A ∩ C c A ∩ C d B ∩ C e C ∪ B f B ∪ C g B ∪ C E.4552 A random experiment consists of randomly drawing a card from a deck of 32 cards. 1 Determine the probabilities of the fol-lowing events : A : ˇ The card drawn is a pique ı ; B : ˇ The card drawn is a figure ı ; C : ˇ The card drawn is noire ı ; D : ˇ The card drawn is valet ı ; 2 Determine the probabilities of the following events : a A ∩ B b A ∩ C c A ∪ B d B ∪ C e C ∩ D f C ∪ D g C ∩ D h C ∪ D 11. Introduction to the probability of a union https://chingmath.fr chapExoCorrec/3052 sacados/3052 NNNNNNNNNNBBNNNNNNNNNNNBBNNBNNNBNNNBBBBNNNNNNNNNNNBBNNNNNNNNNNNBBNNBNNNBNNNBBBBNBNNNBNNNBNBBNBNNNBNNNBNBBNBBNNBBNNBBBBBB chapExoCorrec/3049 sacados/3049 AsAsAsAsRRRRDDDDVVVV10101010999988887777♥♦♠♣ chapExoCorrec/4529 sacados/4529 AsAsAsAsRRRRDDDDVVVV10101010999988887777♥♦♠♣ chapExoCorrec/4552 sacados/4552 AsAsAsAsRRRRDDDDVVVV10101010999988887777♥♦♠♣
AB AB ABAB ABAB E.4513 Consider a random experiment whose universe Ω is shown below. We also consider two events A and B of Ω : The crosses represent the elementary events making up Ω ; each of the elementary events are equiprobable. 1 How many elementary events make up the universe Ω . 2 Determine the probabilities of A and B . 3 a Determine the probabilities of the following two events : A ∪ B ; A ∩ B b Write a relationship between the following probabili-ties : P ( A ) ; P ( B ) ; P ( A ∪ B ) ; P ( A ∩ B ) E.3094 An urn contains twenty balls num-bered from 1 to 20; the first five are red, the next seven are blue and the next eight are yellow. 1 Determine the following probabilities : a A : ˇ The ball drawn carries a number pair ı ; b B : ˇ The ball drawn is rouge ı ; c C : ˇ The ball drawn is red or has a number pair ı ; d D : ˇ The ball drawn is red and has a number pair ı. 2 Does the following equality hold? P A ∪ B = P A + P B Justify your answer. E.3112 Consider a random experiment simu-lating a situation of equiprobability on a universe Ω composed of 11 elementary events. Consider the two events A and B such that : A is composed of 4 elementary events ; B is composed of 8 elementary events ; A ∪ B is composed of 10 elementary events ; 1 a Testing several possibilities, complete the diagram below to realize this situation. b Of how many elementary elements is the event A ∩ B composed. 2 Deduce the following probabilities : a P ( A ) b P ( B ) c P ( A ∩ B ) d P ( A ∪ B ) 3 What relationships can be demonstrated between the probabilities of the events A , B , A ∩ B and A ∪ B ? 12. Probability of a union E.3095 Let Ω ; P be a probabilized space where A and B are two events of Ω such that : P ( A ) = 0.36 ; P ( B ) = 0.27 1 What can we say about A and B if : P A ∪ B =0.63 ? 2 It is assumed that : P A ∪ B =0.5 a What can we say about A and B ? b What is the probability of an event simultaneously re-alizing the events A and B ? E.3100 In a universe Ω provided with the probability law P , consider the two events A and B such that : P ( A ) = 0.37 ; P ( B ) = 0.48 ; P ( A ∪ B ) = 0.62 1 Determine the value of P ( A ∩ B ) . 2 Show below the two assemblies indicated under each of the figures : 3 a Determine the probability of the following events : A ; A ∩ B b Deduce the probability of the event A ∪ B . https://chingmath.fr chapExoCorrec/4513 sacados/4513 AB chapExoCorrec/3094 sacados/3094 chapExoCorrec/3112 sacados/3112 AB chapExoCorrec/3095 sacados/3095 chapExoCorrec/3100 sacados/3100 ABAB ABAB
AB AB E.4553 In a secondary school, a sports event brings together second-year students practicing soccer and basketball. The random experiment considered consists in randomly selecting a student from among the second-year pupils. Consider the two events : F : ˇ Student chooses practice football ı B : ˇ Student chooses practice basketball-ball ı 1 The following probability is given : P ( B ∪ F ) = 0.6 Give the probability of choosing a student participating in this event. 2 The following probabilities are given : P ( F ) = 0.28 ; P ( B ) = 0.22 Knowing that in this school there are 30 second-graders practicing both basketball and soccer, determine the number of second-graders in this school. E.6684 A school offers only two extracurric-ular activities: a drama club and an introductory program-ming workshop. We know that the same number of people are enrolled in these two activities. We randomly select a student in the school and consider the following two events : T : ˇ student is enrolled in club théatre ı P : ˇ Student is enrolled in workshop informatique ı We give the probabilities : P T ∩ P = 0.13 ; P T ∪ P = 0.47 Determine the probability of choosing a student enrolled in the theater club? enrolled in the computer workshop? E.4789 Let Ω ; P be a probabilized space où A and B be two events of Ω such that : P ( A ) = 0.36 ; P ( B ) = 0.27 1 Suppose that the two events A and B verify the relation: P A ∪ B =0.63 ? What can we say about the intersection A ∩ B ? 2 We now assume that : P A ∪ B =0.5 : What is the probability that an event simultaneously re-alizes the events A and B ? E.5907 Consider a random experiment representing a situation of equiprobability. The diagram below shows the elementary events of the universe Ω as well as the two events A and B . Consider an event C of Ω satisfying : P B ∪ C = 5 16 ; P B ∩ C = 2 16 What is the probability of event C ? 2 16 3 16 4 16 5 16 13. Unclassified exercises E.5908 Consider a random experiment representing a situation of equiprobability. The diagram below represents the elemen-tary events of the universe Ω as well as the two events A and B . 1 Determine the probability of the event A ∩ B ? 2 16 3 16 4 16 5 16 2 Consider an event C from Ω verifying: P B ∪ C = 7 16 ; P B ∩ C = 2 16 What is the probability of the event C ? 2 16 3 16 4 16 5 16 E.5910 Consider a six-sided rigged die whose probability law is given in the table below : x 1 2 3 4 5 6 P ( x ) 0.14 0.07 0.2 0.12 0.1 1 What is the probability of the event ˇ the face obtained is the face 6 ı? 0.34 0.35 0.36 0.37 2 Consider the following events : A : ˇ The resulting face is pair ı ; B : ˇ The face has a value strictly greater than 2 ı ; C : ˇ The face has a value less than or equal to 5 ı ; a What is the probability of the event A ? 0.54 0.55 0.56 0.57 b What is the probability of the event B ∩ C ? 0.42 0.44 0.46 0.48 https://chingmath.fr chapExoCorrec/4553 sacados/4553 chapExoCorrec/6684 sacados/6684 chapExoCorrec/4789 sacados/4789 chapExoCorrec/5907 sacados/5907 AB chapExoCorrec/5908 sacados/5908 AB chapExoCorrec/5910 sacados/5910