Aspire Faculty ID #17245 · Topic: CUET UG 2022 Applied Mathematics · Just now
CUET UG 2022 Applied Mathematics

For two events $A, B$

$P(A\cup B)=\frac{7}{12}, ; P(A)=\frac{5}{12}, ; P(B)=\frac{3}{12}$

Then $P(A\cap B)=$

Solution

We know,

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

Substitute values:

$\frac{7}{12}=\frac{5}{12}+\frac{3}{12}-P(A\cap B)$

$\frac{7}{12}=\frac{8}{12}-P(A\cap B)$

So,

$P(A\cap B)=\frac{8}{12}-\frac{7}{12}$

$=\frac{1}{12}$

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