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Previous Year Question (PYQs)



Let $A_1,A_2,A_3$ are three events in a sample space with the condition $A_1\cap A_2\neq \phi$, then always:





Solution

By multiplication rule of probability,

$P(A_1\cap A_2)=P(A_1)P(A_2/A_1)$

Now,

$P(A_1\cap A_2\cap A_3)=P(A_1\cap A_2)P(A_3/(A_1\cap A_2))$

Substituting the value of $P(A_1\cap A_2)$,

$P(A_1\cap A_2\cap A_3)=P(A_1)P(A_2/A_1)P(A_3/(A_1\cap A_2))$



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