Answer to Question #207242 in Statistics and Probability for Kll

Question

even A and B are such that P(A U B )=0.76,P(B)=0.4 Given that A and B are non mutually exclusive events that are independent calculate P(A)

Answer 1

$A$ and $B$ are non mutually events: $P(A\cap B)\not=0.$

$A$ and $B$ are independent events: $P(A\cap B)=P(A)P(B).$

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

$$=P(A)+P(B)-P(A)P(B)$$

$$P(A)=\dfrac{P(A\cup B)-P(B)}{1-P(B)}$$

$$=\dfrac{0.76-0.4}{1-0.4}=0.6$$

$P(A)=0.6$