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Question

Check whether the following probabilities P(A) and P(B) are consistently defined
(i) P(A)=0.5,P(B)=0.7, P(AB)=0.6
(ii) P(A)=0.5,P(B)=0.4, P(AB)=0.8

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Solution

(i) P(A)=0.5,P(B)=0.7, P(AB)=0.6
It is known that if E and F are two events such that EF then P(E)P(F)
However here P(AB)>P(A)
Hence P(A) and P(B) are not consistently defined
(ii) P(A)=0.5,P(B)=0.4, P(AB)=0.8
It is known that if E and F are two events such that EF then P(E)P(F)
Here it is seen that P(AB)>P(A)andP(AB)>P(B)
Hence P(A) and P(B) are consistently defined

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