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Question

If P(AC)>P(BC) and P(A¯C)>P(B¯C) then the relationship between P(A) and P(B) is

A
P(A)=P(B)
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B
P(A)P(B)
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C
P(A)>P(B)
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D
P(A)P(B)
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Solution

The correct option is A P(A)>P(B)
P(AC)=P(AC)P(C)
Now 0<P(C)<1
Also,
P(BC)=P(BC)P(C)
Now
P(AC)>P(BC)
P(AC)P(C)>P(BC)P(C)
Hence
P(AC)>P(BC) ...(i)
P(A)P(AC)>P(B)P(BC)
Now P(A)>P(B)+P(AC)P(BC)
P(A)>P(B)

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