consider the following scenario

Question

Consider the following scenario:

• Let P(C) = 0.5

• Let P(D) = 0.6

• Let P(C | D) = 0.7

Part (a)

Find P(C AND D).

Part (b)

Are C and D mutually exclusive? Why or why not?

A. C and D are not mutually exclusive because P(C AND D) ≠ 0

.B. There is not enough information to determine if C and D are mutually exclusive.

C. C and D are not mutually exclusive because P(C) + P(D) ≠ 1

.D. C and D are mutually exclusive because they have different probabilities.

Part (c)

Are C and D independent events? Why or why not?

A.The events are not independent because the sum of the events is less than 1.

B.The events are not independent because P(C | D) ≠ P(C)

. C.The events are not independent because P(C) × P(D) ≠ P(C | D)

. D.The events are independent because they are mutually exclusive.

Part (d)

Find P(D | C).

Answer 1

a) P(C and D) = P(C|D) * P(D) = 0.7 * 0.6 = 0.42

b) C and D are not mutually exclusive because P(C AND D) ≠ 0 (the probability of both C and D occurring at the same time is non-zero).

c) The events are not independent because P(C | D) ≠ P(C). If they were independent, the probability of C would not be conditioned on D occurring.

d) P(D|C) = P(C and D)/P(C) = 0.42/0.5 = 0.84