Question

Let ( p(c) = 0.4 ), ( p(D) = 0.5 ), ( p(c|d) = 0.6 ). Find ( p(c text( and ) d) ).

A) 0.24
B) 0.30
C) 0.36
D) 0.20

Answer 1

The probability of event C and D occurring together (p(c and d)) is 0.24. (Option A)

Step-by-step explanation:

We can use the formula for conditional probability: p(c and d) = p(c|d) * p(d).

Given:

p(c) = 0.4 (probability of event C)

p(d) = 0.5 (probability of event D)

p(c|d) = 0.6 (probability of event C given that D occurred)

Plugging these values into the formula:

p(c and d) = 0.6 * 0.5 = 0.30

However, the question asks for the probability of both C and D occurring simultaneously, not necessarily C occurring given D. Therefore, we need to adjust the calculation.

p(c and d) = p(c) * p(d) = 0.4 * 0.5 = 0.20

Therefore, the correct answer is A) 0.20.