Question

According to the general equation for conditional probability, if P(AB) =
4/5
and P(B) = 5/6, what is P(AIB)?
A.15/16
B.35/36
C.8/9
D.24/25

Answer 1

Answer:

$\sf D. \quad P(A|B)=\dfrac{24}{25}$

Step-by-step explanation:

General equation for conditional probability

$\sf P(A \cap B)=P(A)\:P(B|A)$

As we need to find P(A|B) we can rewrite the equation:

$\implies \sf P(B \cap A)=P(B)\:P(A|B)$

Given:

     $\sf P(A \cap B)=\dfrac{4}{5}$

     $\sf P(B)=\dfrac{5}{6}$

Remember that $\sf P(A \cap B)=P(B \cap A)$

Substitute the given values into the formula:

$\implies \sf P(B \cap A)=P(B)\:P(A|B)$

$\implies \sf \dfrac{4}{5}=\dfrac{5}{6}\:P(A|B)$

$\implies \sf P(A|B)=\dfrac{4}{5} \div \dfrac{5}{6}$

$\implies \sf P(A|B)=\dfrac{4}{5} \times \dfrac{6}{5}$

$\implies \sf P(A|B)=\dfrac{24}{25}$