SOLUTION: The probability of C is 0.25. The conditional probability that C occurs given that D occurs is 0.3. The conditional probability that C occurs given that D does not occur is 0.2.

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Question 745392: The probability of C is 0.25. The conditional probability that C occurs given that D occurs is 0.3. The conditional probability that C occurs given that D does not occur is 0.2.
(a) What is the probability that D occurs?

(b) What is the conditional probability that D occurs given that C occurs?

Answer by stanbon(75887) (Show Source):
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The probability of C is 0.25. The conditional probability that C occurs given that D occurs is 0.3. The conditional probability that C occurs given that D does not occur is 0.2.
(a) What is the probability that D occurs?
P(C and D) = 0.3*P(D)
P(C and D') = 0.2*P(D')
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Add to get:
P(C) = 0.3P(D) + 0.2(1-P(D))
0.25 = 0.3P(D) + 0.2 - 0.2P(D)
0.05 = 0.1P(D)
P(D) = 0.5
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(b) What is the conditional probability that D occurs given that C occurs?
P(D | C) = P(C and D)/P(C)
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P(C and D) = 0.3*P(D) = 0.3*0.5 = 0.15
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So, P(D | C) = 0.15/0.25 = 3/5 = 0.6
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cheers,
Stan H.