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;

$P(A|B)\text{ = }\frac{P(A\cap B)}{P(B)}$

We are given the values of the two;

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

Substituting the values into the formula we have;

$\begin{gathered} P(A|B)\text{ =}\frac{(\frac{3}{7})}{(\frac{7}{8})}=\text{ }\frac{3}{7}\times\frac{8}{7}=\text{ }\frac{24}{49} \\ P(A|B)\text{ = }\frac{24}{49} \end{gathered}$

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

$P(A|B)\text{ = }\frac{24}{49}$

Answer is D