Consider an experiment with events A, B, and C for which P(A)= 0.23, P(B)= 0.40,

游客2025-02-23 47

问题 Consider an experiment with events A, B, and C for which P(A)= 0.23, P(B)= 0.40, and P(C)= 0.85. Suppose that events A and B are mutually exclusive and events B and C are independent. What are the probabilities P(A or B)and P(B or C)?

选项

答案 0.63
0.91

解析 Since A and B are mutually exclusive,
P(A or B)= P(A)+ P(B)= 0.23 + 0.40 = 0.63
Since B and C are independent, P(B and C)= P(B)P(C). So,
P(B or C)= P(B)+ P(C)- P(B and C)= P(B)+ P(C)- P(B)P(C)
Therefore,
P(B or C)= 0.40 + 0.85 -(0.40)(0.85)= 1.25 - 0.34
= 0.91

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