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Question

Suppose A and B are two events with P(A)=0.5 and P(AB)=0.8. Let P(B)=p if A and B are mutually exclusive and P(B)=q if A and B are independent events, then the value of q/p is

A
2
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B
1
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C
3
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D
0.1
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Solution

The correct option is C 2
P(A)=0.5 and P(AB)=0.8
When A and B are independent events,
P(AB)=P(A)×P(B)
P(A)+P(B)P(AB)=0.5×q
0.5+q0.8=0.5q
0.5q=0.3
q=0.6
When A and B are mutually exclusive events
P(AB)=0
P(A)+P(B)=P(AB)
0.5+p=0.8
p=0.3
Hence the ratio of q and p is 2

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