Key concepts:

- P(X or Y) = P(X) + P(Y) - P(X and Y)

- If X and Y are mutually exclusive events, then P(X and Y) = 0

- If X and Y are independent events, then P(X and Y) = P(X) * P(Y)


(a) Find P(B)
Since events A and B are mutually exclusive, we know that P(A and B) = 0
Take: P(A or B) = P(A) + P(B) - P(A and B) and replace parts with their given values.
We get: 0.6 = 0.2 + P(B) - 0
Solve to get: P(B) = 0.4

Answer: 0.4

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(b) Find P(D)
Since events C and D are mutually exclusive, we know that P(C and D) = P(C) x P(D)
Take: P(C or D) = P(C) + P(D) - P(C and D) and replace parts with their given values.
We get: 0.6 = 0.5 + P(D) - [0.5 x P(D)]
Subtract 0.5 from both sides to get: 0.1 = P(D) - [0.5 x P(D)]
Factor out P(D) to get: 0.1 = P(D)[1 - 0.5]
Simplify to get: 0.1 = P(D)[0.5]

Divide both sides by 0.5 to get: P(D) = 0.1/0.5 = 1/5 = 0.2

Answer: 0.2

Cheers,
Brent
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