(a) To get to the university campus you must take two buses. The first bus runs with probability k+2 where k is the last non-zero digit of your 4k student ID number. The second bus runs with probability 3/4. Moreover, the kind people at Transport for London always ensure that at least one of the buses is running. Given that the second bus is running, what is the probability that the first bus is not. (b) Let E₁ and E2 be events with P(E₁) > 0 and P(E₂) > 0. Prove that if P(E₁|E₂) > P(E₁) then P(E2|E1) > P(E2).

(a) To get to the university campus you must take two buses. The first bus runs with probability k+2 where k is the last non-zero digit of your 4k student ID number. The second bus runs with probability 3/4. Moreover, the kind people at Transport for London always ensure that at least one of the buses is running. Given that the second bus is running, what is the probability that the first bus is not. (b) Let E₁ and E2 be events with P(E₁) > 0 and P(E₂) > 0. Prove that if P(E₁|E₂) > P(E₁) then P(E2|E1) > P(E2).

College Algebra

7th Edition

ISBN:9781305115545

Author:James Stewart, Lothar Redlin, Saleem Watson

Publisher:James Stewart, Lothar Redlin, Saleem Watson

Chapter9: Counting And Probability

Section9.2: Probability

Problem 31E

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