A and B are two events such that P(A)=0.54 , P(B)=0.69 and P(A cap B)=0.35. Find P left(

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14.Probability

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$A$ and $B$ are two events such that $P(A)=0.54$, $P(B)=0.69$ and $P(A \cap B)=0.35.$ Find $P \left( B \cap A ^{\prime}\right)$.

A

$0.34$

B

$0.34$

C

$0.34$

D

$0.34$

Solution

It is given that $P ( A )=0.54$, $P ( B )=0.69$, $P (A \cap B)=0.35$

We know that

$n\left( B \cap A ^{\prime}\right)=n( B )-n( A \cap B )$

$\Rightarrow \frac{n\left( B \cap A ^{\prime}\right)}{n( S )}$ $=\frac{n( B )}{n( S )}-\frac{n( A \cap B )}{n( S )}$

$\therefore P \left( B \cap A ^{\prime}\right)= P ( B )- P ( A \cap B )$

$\therefore P \left( B \cap A ^{\prime}\right)=0.69-0.35=0.34$

Standard 11

Mathematics

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