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The following applies to questions 4-6 below. Assume the following notation: p(A) is the probability of event A; P(AB) is the probability of A and B; p(AVB) is the probability of A or B; p(AB) is the probability of A given B; S is the universe of possibilities; -A is the negation of A; and is the null event.

4. p(AB) where xis A. p(A) P(B) B. P(AlB)p(B) C. p(BIA) D. p(B)2 E. p(A V B) 5. For all A in S, p(A) where z is B. V/2 C. 0 D. 0.75 E. 0.5 6. For all A in S, p(A) where r is A. 0.5 B. 1 D. 0 E. 0.25

19. Assume the following notation: p(A) is the probability of event A; p(AB) is the probability of A and B; p(AV B) is the probability of A or B; p(AB) is the probability of A given B; S is the universe of possibilities; -A is the negation of A; and Ø is the null event. If and only if p(A v B) = p(A) + p(B), p(AB) = x where x is B. 0.5 C. 0 D. 1 E. 0.25

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Answer #1

(4) p(AB) = x = p(A|B)p(B), derived from conditional probability formula.

(5) For all A in S, p(A) >= 0.

(6) For all A in S, p(A) <= 1.

(19) p(AB) = 0, since A and B are mutually exclusive events here.

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