Question

Watch help videoIn a class of students, the following data table summarizes the gender of the studentsand whether they have an A in the class. What is the probability that a student is amale given that they have an A?Female MaleHas an A42Does not have an A167Answer:Submit Answerattempt 1 out of 5/problem 1 out of max 1MacBook Pro

Answer 1

Consider the following events,

M = selected student is a male

F = selected student is a female

A = selected student has an A

The probability that the student is a male, given that he/she has an A, is given by,

$P(\frac{M}{A})=\frac{P(M\cap A)}{P(A)}$

This can be evaluated as,

$\begin{gathered} P(\frac{M}{A})=\frac{P(M\cap A)}{P(A)} \\ P(\frac{M}{A})=\frac{n(M\cap A)}{n(A)} \\ P(\frac{M}{A})=\frac{2}{4+2} \\ P(\frac{M}{A})=\frac{2}{6} \\ P(\frac{M}{A})=\frac{1}{3} \end{gathered}$

Thus, the probability that the student is a male, is 1/3 , given that he/she has an A.