solution for c2 C1. Let A and B be two events with P(A) = 0.8 and P(B) = 0.4. The following questions concern thevalue of P(An B), the probability that both A and B occur.(a) Prove the upper bound P(AN B) < 0.4.(b) Prove that this upper bound can be achieved, by giving an example of a sample space N, aprobability measure P and events A, B CN such that P(A) = 0.8 and P(B) = 0.4, with equalityP(AN B) = 0.4 in the upper bound.(c) Give a lower bound for P(AN B) – that is, prove that P(A n B) > something – and show thatthis lower bound can be achieved. (Try to work out the correct bound, even if you can't formallyprove it.)C2. A “random digit" is a number chosen at random from {0,1, ...,9}, each with equal probability. Astatistician choses n random digits.(a) For k = 0, 1,... , 9, let A be the event that all the digits are k or smaller. What is the probabilityof A, as a function of k and n?(b) Let Br be the event that the largest digit chosen is equal to k. What is the probability of B?Justify your answer carefully.

Answered: Image /qna-images/answer/69dc6028-b570-44a0-b98e-ce0643d4e219.jpg

C2. A “random digit" is a number chosen at random from {0,1,..., 9}, each with equal probability. A statistician choses n random digits. (a) For k = 0, 1, . .. , 9, let A be the event that all the digits are k or smaller. What is the probability of Ak, as a function of k and n? (b) Let Bå be the event that the largest digit chosen is equal to k. What is the probability of B½? Justify your answer carefully.

C2. A “random digit" is a number chosen at random from {0,1,..., 9}, each with equal probability. A statistician choses n random digits. (a) For k = 0, 1, . .. , 9, let A be the event that all the digits are k or smaller. What is the probability of Ak, as a function of k and n? (b) Let Bå be the event that the largest digit chosen is equal to k. What is the probability of B½? Justify your answer carefully.

College Algebra

7th Edition

ISBN:9781305115545

Author:James Stewart, Lothar Redlin, Saleem Watson

Publisher:James Stewart, Lothar Redlin, Saleem Watson

Chapter9: Counting And Probability

Section9.3: Binomial Probability

Problem 2E: If a binomial experiment has probability p success, then the probability of failure is...

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