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Question

Events A, B and C satisfy P(A)=0.3, P(B)=0.3, P(C)=0.5. If events A and B are mutually exclusive, events A and C are independent, and P(B|C)=0.2, then 300P(ABC) equals

A
255
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B
255.00
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C
255.0
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Solution

P(B|C)=0.2, P(A)=0.3, P(B)=0.3, P(C)=0.5
P(B|C)=P(BC)P(C)
P(BC)=P(B|C)P(C)=0.2×0.5=0.1
Event A and C are independent.
P(AC)=P(A)×P(C)=0.3×0.5=0.15
Events A and B are mutually exclusive.
P(AB)=0P(ABC)=0

P(ABC)
=P(A)+P(B)+P(C)P(BC)P(AC)
=0.3+0.3+0.50.10.15=0.85

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