Question

If A and B are two independent events such that $P\left(A\cup B\right)=0.75andP\left(B\right)=0.25,P\left(A\right)=.......$

• A. $\frac{2}{3}$
• B. $\frac{1}{3}$
• C. $\frac{1}{2}$
• D. NONE OF THESE

Answer 1

The correct option is A $\frac{2}{3}$

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

$SinceAandBareindependenteventsP(A\cap B)=P\left(A\right)P\left(B\right)$

$0.75=P\left(A\right)+0.25-0.25P\left(A\right)$

$P\left(A\right)=0.5/0.75=2/3$