Question

Consider the following scenario: Let P(C) = 0.4. Let P(D) = 0.5. Let P(C|D) = 0.6. a. Find P(C AND D). b. Are C and D mutually exclusive? Why or why not? c. Are C and D independent events? Why or why not? d. Find P(C OR D). e. Find P(D|C).

Answer 1

a. By definition of conditional probability,

P(C | D) = P(C and D) / P(D)  ==>  P(C and D) = 0.3

b. C and D are mutually exclusive if P(C and D) = 0, but this is clearly not the case, so no.

c. C and D are independent if P(C and D) = P(C) P(D). But P(C) P(D) = 0.2 ≠ 0.3, so no.

d. Using the inclusion/exclusion principle, we have

P(C or D) = P(C) + P(D) - P(C and D)  ==>  P(C or D) = 0.6

e. Using the definition of conditional probability again, we have

P(D | C) = P(C and D) / P(C)  ==>  P(D | C) = 0.75