Question

Consider the following scenario:

Answer 1

Answer:

1. P(C AND D) = 0.3

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

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

4.P(D | C) = 0.5

Step-by-step explanation:

• Let P(C) = 0.4

• Let P(D) = 0.5

• Let P(C | D) = 0.6

1.) Find P(C AND D).

$P(C | D) = \frac{P(C n D)}{P(D)} \\P(C n D) = P(C | D) * P(D)\\P(C n D) = 0.6 * 0.5\\P(C n D) = 0.3$

2.) Events can be mutually exclusive meaning the both event cannot happen at the same time. So, P(A and B) = 0

3.) Events can be "Independent", meaning each event is not affected by any other events.

4.) Find P(D | C)

$P(D | C) = \frac{P (D n C)}{P(C)}\\P(D n C) = 0.5 * 0.4 = 0.2\\P(D | C) = \frac{0.2}{0.4}\\P(D | C) = 0.5$