Question

A test was given to a group of students. The grades and gender are summarized below A B C TotalMale4192043Female1116532Total15352575If one student is chosen at random from those who took the test,Find the probability that the student got a 'B' GIVEN they are male.

Answer 1

`\begin{gathered} P(A)=Probability\text{ that the student got a B} \\ P(B)=\text{Probability that the student are male} \\ P(A|B)=\text{Probability that the student got a B given they are male} \\ P(A|B)=(P(A\cap B))/(P(B)) \\ P(A\cap B)=Probability\text{ that the student got a B and be male} \\ \text{From the table} \\ P(A\cap B)=(19)/(75) \\ P(B)=(43)/(75) \\ \\ P(A|B)=((19)/(75))/((43)/(75)) \\ P(A|B)=(19)/(43)=0.442=44.2\text{ \%} \\ \text{The probability is }(19)/(43)=0.442=44.2\text{ \%} \end{gathered}`