G and H are mutually exclusive events

Question

G and H are mutually exclusive events.

• P(G) = 0.5

• P(H) = 0.3

Part (a)

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

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

D.The statement is false because P(H | G) = P(H)/P(G) = 0.6.

Part (b)

Find P(H OR G).

Part (c)

Are G and H independent or dependent events? Explain.

A.G and H are independent events because they are mutually exclusive.

B.There is not enough information to determine if G and H are independent or dependent events.

C.G and H are dependent events because they are mutually exclusive.

D.G and H are dependent events because P(G OR H) ≠ 1.

Answer 1

a) P(H | G) = 0.4 must be false because P(H | G) = P(H and G)/P(G). If H and G are mutually exclusive, then if G occurred, H cannot happen. This means that P(H and G) = 0 - ie H and G cannot happen at the same time. Thus, P(H | G) = 0. The answer choice is A.

b) We can use the general addition rule to find P(G or H):

P(G or H) = P(G) + P(H) _ P(G and H)

P(G or H) = 0.5 = 0.3 - 0

P(G or H) = 0.8

Note: an important concept is that when events are mutually exclusive, you can simply add their probabilities to get the "or" probability of the events.

c) G and H are dependent because knowing that G happened, tells us something about the P(H) since they are mutually exclusive. In other words, the probability of H changes if G has occurred. The probability of H depends on whether or not G occurred. The probability of G also depends on whether or not H as occurred. So the answer choice in the case is C.

Note: Events that are mutually exclusive cannot be independent and events that are independent cannot be mutually exclusive. However, there are many events that are neither mutually exclusive nor independent.