Grade 12 - Comp. / Annales probabilités 3 exercises (100% corrected)

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:::SSF::::::S:::SF 1. Binomial law E.6981 Notations: For any event A , we denote A as the opposite event of A and p ( A ) as the probability of event A . If A and B are two events, we denote p B ( A ) as the proba-bility of A given that event B has occurred. Note: In this exercise, we will round the results to three decimal places. Parts A and B are independent. A temporary employment agency studies all job seekers ac-cording to two criteria: gender and professional experience. This study shows that : 52 % of job seekers are women and 48 % are men ; 18 % of job seekers have no experience and the rest have experience ; among the men who are job seekers, we know that 17 ; 5 % have no experience. Part A We randomly select the file of a job seeker from this agency. We note : S : the event ˇ the job seeker has no experience ı ; F : the event ˇ the job seeker is a woman ı 1 Specify p ( S ) and p F ( S ) . 2 Copy the tree below and fill in the dotted lines with the associated probabilities 3 Prove p F ∩ S =0 ; 084 . Interpret the result. 4 The file selected is that of a job seeker with no experience. Calculate the probability that it is a man. 5 Knowing that the file selected is that of a woman, calcu-late the probability that it is the file of a job seeker with no experience. Part B The agency manager decides to review the situation with five job seekers who are being monitored by her agency. To do this, she selects five files at random. We assume that the number of job seekers in her agency is large enough to treat this situation as a draw with replacement. Justifying your reasoning, calculate the probability that, among the five files drawn at random, there is at least one file of a job seeker without experience. E.7213 Note: This exercise is a MCQ (multiple-choice quizz) . For each question, only one of the four answers is correct. Copy the question number and the correct answer. No justifi-cation is required. A correct answer is worth one point ; a wrong answer or no answer is worth neither points nor penalties. Probabilities are given to the nearest 0 ; 001 . For the Boisjoli village festival, the mayor invited children from neighboring villages. The town hall services that managed the registrations counted 400 children at this festival; they also indicated that 32 % of the children present were children who live in the village of Boisjoli. 1 The number of children from neighboring villages is : a 128 b 272 c 303 d 368 During the party, eight children are chosen at random to form a team that will participate in a sports challenge. We assume that the number of children is large enough for this situation to be considered a random draw with replacement. Let X be the random variable taking values equal to the num-ber of children on the team who live in the village of Boisjoli. 2 The random variable X follows the binomial distribution with parameters a n =400 et p =0 ; 32 b n =8 et p =0 ; 32 c n =400 et p =8 d n =8 et p =0 ; 68 3 The probability that there is at least one child in the team who lives in the village of Boisjoli is : a 0 ; 125 b 0 ; 875 c 0 ; 954 d 1 4 The mathematical expectation of X is : a 1 ; 4708 b 2 ; 56 c 87 ; 04 d 128 E.7116 From a population survey, it was found that : 60 % of the population are women ; 56 % of women work part-time ; 36 % of the population work part-time. One person in the population is interviewed. She states that she works part-time. What is the probability that this person is a man? https://chingmath.fr chapExoCorrec/6981 sacados/6981 Liban Juin 2017 :::SSF::::::S:::SF chapExoCorrec/7213 sacados/7213 chapExoCorrec/7116 sacados/7116 Asie Juin 2016