Question

According to the general equation for conditional probability, if P(AnB) =3/7and P(B) =7/8, what is P(A | B)?A.32/49B.40/49C.16/49D.24/49

Answer 1

Recall that the formula for conditional probability is;

`P(A|B)\text{ = }(P(A\cap B))/(P(B))`

We are given the values of the two;

`\begin{gathered} P(A\cap B)\text{ = }(3)/(7) \\ P(B)\text{ = }(7)/(8) \end{gathered}`

Substituting the values into the formula we have;

`\begin{gathered} P(A|B)\text{ =}(((3)/(7)))/(((7)/(8)))=\text{ }(3)/(7)*(8)/(7)=\text{ }(24)/(49) \\ P(A|B)\text{ = }(24)/(49) \end{gathered}`

So, the conditional probability P(A | B) is;

`P(A|B)\text{ = }(24)/(49)`

Answer is D