Question

According to the general equation for conditional probability, if P(A^B) = 2/9 and P(B)=1/3, what is P(A|B)?

Answer 1

Answer: B.
`(2)/(3)`

Explanation:

We know that the formula to find the conditional probability of A given that B is given by :-

`P(A|B)=(P(A\cap B))/(P(B))`

Given :
`P(A\cap B)=(2)/(9)`

`P(B)=(1)/(3)`

Then , the conditional probability of A given that B is given by :-

`P(A|B)=((2)/(9))/((1)/(3))\\\\\Rightarrow\ P(A|B)=(2)/(3)`

Answer 2

So, Option B is correct.

Explanation:

Considering A and B are independent events

The formula used for:

P(A|B) = P(A∩B) / P(B)

P(A∩B) = 2/9

P(B) = 1/3

Putting the values in formula:

P(A|B) = P(A∩B) / P(B)

P(A|B) = 2/9 / 1/3

P(A|B) = 2/9 * 3

p(A|B) = 2/3

So, Option B is correct.