A sample space S yields four simple events A B C and D such

A sample space, S, yields four simple events, A, B, C, and D, such that P(A) = 0.40, P(B) = 0.22, and P(C) = 0.23.

Find P(D). (Do not round intermediate calculations. Round your answer to 2 decimal places.)

  P(D)

Solution

a)

The simple events must add up to a probability of 1.

Thus,

0.4 + 0.22 + 0.23 + P(D) = 1

0.85 + P(D) = 1

P(D) = 0.15 [ANSWER]

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B)

P(Cc) = 1 - P(C) = 1 - 0.23 = 0.77 [ANSWER]

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C)

P(A U B) = P(A) + P(B) = 0.40 + 0.22 = 0.62 [ANSWER]