# 12.(ii)     Check whether the following probabilities  $P(A)$  and  $P(B)$  are consistently defined   (ii)   $P(A)=0.5,P(B)=0.4,P(A\cup B)=0.8$

H Harsh Kankaria

(ii)   Given, $P(A)=0.5,P(B)=0.4,P(A\cup B)=0.8$

We know,

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

$\implies$ 0.8 = 0.5 + 0.4 - P(A $\cap$ B)

$\implies$ P(A $\cap$ B) = 0.9 - 0.8 = 0.1

Therefore, P(A $\cap$ B) < P(A) and P(A $\cap$ B) < P(B) , which satisfies the condition.

Hence, the probabilities are consistently defined

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