Question

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

P(A)=1/2 P(A and B)=1/6
1/4
1/8
3/4
1/3

EDIT: Nevermind, I figured it out, to those who want to know the answer is it's 1/3 :)

Answer 1

Answer: the value of P(B) =
`(1)/(3)` .

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)=(1)/(2),\ \ P(\text{A and B})=(1)/(6)`

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

Put all values in (i), we get

`(1)/(6)=(1)/(2)* P(B)\\\\\Rightarrow\ P(B)=(2)/(6)\\\\\Rightarrow\ P(B)=(1)/(3)`

Hence, the value of P(B) =
`(1)/(3)` .