Question

Given the following probabilities, for what P(B) are events A and B independent?

Answer 1

Answer: the value of P(B) = $\dfrac{1}{3}$ .

Step-by-step explanation:

If A and B are two independent events, then P(A and B)=P(A) x P(B)  (i)

Given the following probabilities : $P(A)=\dfrac{1}{2},\ \ P(\text{A and B})=\dfrac{1}{6}$

To find : $P(B)$ such that events A and B are independent

Put all values in (i), we get

$\dfrac{1}{6}=\dfrac{1}{2}\times P(B)\\\\\Rightarrow\ P(B)=\dfrac{2}{6}\\\\\Rightarrow\ P(B)=\dfrac{1}{3}$

Hence, the value of P(B) = $\dfrac{1}{3}$ .