G and H are mutually exclusive events. P(H)-0.3 Part (a) Explain why the followi

Question

G and H are mutually exclusive events. P(H)-0.3 Part (a) Explain why the following statement MUST be false: PHI G)0.4 To find conditional probability, divide P(G AND H) byM), which gives 0.5. The statement is false because PH | G)·rm-0.6. The events are mutually exclusive, which means they can be added together, and the sum is not 0.4. The events are mutually exclusive, which makes PlH AND G-0; therefore, P(H 1 G)-0. O PKG) Part(b) Find PH OR G) Part (c) Are G and H independent or dependent events? Explain. G and H are dependent events because they are mutually exclusive. G and H are dependent events because BG OR H-1. There is not enough information to determine if G and H are independent or dependent events. G and Hare independent events because they are mutually exclusive.

Explanation / Answer

Given, G and H are mutually exclusively events

P (G) =0.5

P (H) =0.3

Consider P (H G) =0 {since for mutually exclusive events, the events cannot be occur both}

Part a) P (H/G) = 0.4

d) The events are mutually exclusive which makes P (H and G) = 0, therefore P (H/G) = 0

Part b) P (H or G)

P (H or G) = P (H) + P (G) - P (H and G) = 0.3+0.5-0 = 0.8

P (H or G) = 0.8

Part c) Are G and H independent or dependent events. Explain?

Since probabilities of G and H are non-zero and mutually exclusive events, P (A)* P (B) 0 which says that events are dependent

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