Question

14. Suppose a math class contains 35 students, 17 females (five of whom speak French) and 18 males (three of whom speak French). Compute the probability that a randomly selected student speaks French, given that the student is male.

Answer 1

The formula to calculate the conditional probability of A given B is given to be:

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

If French is represented by F, and males by M, the formula to calculate the probability of a student speaking French given they are male is given to be:

$P(F|M)=\frac{P(F\cap M)}{P(M)}$

The probability formula is given to be:

$P(A)=\frac{n(A)}{n(T)}$

Therefore, we have:

$\begin{gathered} P(F\cap M)=\frac{n(F\cap M)}{n(Students)} \\ n(F\cap M)=students\text{ that speak french and are male}=3 \\ n(Students)=35 \\ \therefore \\ P(F\cap M)=\frac{3}{35} \end{gathered}$

and

$P(M)=\frac{18}{35}$

Therefore, the conditional probability is:

$\begin{gathered} P(F|M)=\frac{\frac{3}{35}}{\frac{18}{35}}=\frac{3}{35}\times\frac{35}{18} \\ P(F|M)=\frac{3}{18}=\frac{1}{6}=0.167 \end{gathered}$

The probability is 0.167 or 1/6