Explain why the following statement MUST be false: P(H | G) = 0.4

Question

G and H are mutually exclusive events.

• P(G) = 0.5

• P(H) = 0.3

Explain why the following statement MUST be false: P(H | G) = 0.4.

A) The events are mutually exclusive, which makes P(H AND G) = 0; therefore, P(H | G) = 0.

B) The statement is false becauseP(H | G) = P(H AND G) = 0.6.    To find conditional probability, divide P(G AND H) by P(H)

C) To find conditional probability divide P(G AND H) by P(H), which gives 0.5

D) The events are mutually exclusive, which means they can be added together, and the sum is not 0.4.

Answer 1

The answer should be A.

They are mutually exclusive, which means they have nothing in common (in a venn diagram), so they cannot be added together.

Then, P(H and G) = 0

P(H | G) = P(H and G)/P(G) = 0/0.5 = 0