Question
The probability that a student takes an English class and a math class is 0.084. The probability that a student takes an English class is 0.49. What is the probability that a student takes a math class, given that the student is taking an English class?
Solution
Let E denotes the event that the student takes an English class
Let M denotes the event that the student takes a Math class
We are given
[tex]\begin{gathered} p(E\cap M)=0.084 \\ p(E)=0.49 \end{gathered}[/tex]We want to find
[tex]p(M|E)[/tex]The formula to use is given as
[tex]p(M|E)=\frac{p(M\cap E)}{p(E)}[/tex][tex]\begin{gathered} p(M|E)=\frac{p(M\cap E)}{p(E)} \\ p(M|E)=\frac{0.084}{0.49} \\ p(M|E)=0.1714 \\ p(M|E)=0.171 \end{gathered}[/tex]Thus, the answer is 0.171
Option D
