Question

1. Check whether the following probabilities P (A) and P (B) are consistently defined : (i) P (A) = 0.5, P (B) = 0.7, P (A n B) = 0.06
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Answer 1

Answer:

See explanation

Step-by-step explanation:

• We know for any two events A and B of sample space

        $P(A\cup B)=P(A)+P(B)-P(A\cap B)$

Here given $P(A)=0.5,P(B)=0.7, P(A\cap B)=0.06$

     $\Rightarrow P(A\cap B)=0.5+0.7-0.06=1.2-0.06=1.14>1$

But we also know probability of any event can not be greater than 1.

Hence given probabilities are not consistently defined