Question

A and B are two mutually exclusive and exhaustive events. If $P\left(A\right)=\frac{1}{7}$ find the value of $49\times P\left(B\right)$.

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Answer 1

we are given the two events are mutually exclusive and exhaustive.

Mutually exclusive $\Rightarrow P(A\cap B)=0$

Exhaustive $\Rightarrow P(A\cup B)=1$

$P(A\cup B)=1$

$\Rightarrow P\left(A\right)+P\left(B\right)-P(A\cap B)=1$

But $P(A\cap B)=0$

$\Rightarrow P\left(A\right)+P\left(B\right)=1$

$\Rightarrow P\left(B\right)=1-P\left(A\right)$

=$1-\frac{1}{7}$

=$\frac{6}{7}$

$\Rightarrow$ Answer =$49\times \frac{6}{7}$

=42