Question

$AandBaremutuallyexclusiveeventsofanexperiment.$
$IfP\left(\overline{A}\right)=0.65,P(A\cup B)=0.65andP\left(B\right)=P.$
$FindthevalueofP.$

• A. 0.70
• B. 0.30
• C. 0.63
• D. 0.35

Answer 1

The correct option is B 0.30

$WeknowP\left(A\right)=1-P\left(\overline{A}\right)$

$=1-0.65=0.35and$

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

$\Rightarrow 0.65=0.35+P\left(B\right)-0$

$\because AandBaremutuallyexclusiveevents$

$\Rightarrow P\left(B\right)=0.65-0.35=0.30$