Question

In a certain town, $40\%$ of the people have brown hair,$25\%$ have brown eyes and$15\%$ have both brown hair and brown eyes. If a person selected at random from the town, has brown hair, the probability that he also has brown eyes is

• A. $\frac{1}{5}$
• B. $\frac{3}{8}$
• C. $\frac{1}{3}$
• D. $\frac{2}{3}$

Answer 1

The correct option is B

$\frac{3}{8}$

Explanation for the correct option:

Finding the probability:

Let $A$ be the people that have brown hair and $B$ be the event that the people have brown eyes.

Then,

$$\begin{gathered} P\left(A\right)=40\% \\ =\frac{40}{100} \\ P\left(B\right)=25\% \\ =\frac{25}{100} \\ P(A\cap B)=15\% \\ =\frac{15}{100} \end{gathered}$$

Therefore, the required probability that a person has brown hair and brown eyes $=\mathrm{P}(\mathrm{B}/\mathrm{A})$

$$\begin{gathered} P\left(\frac{B}{A}\right)=\frac{\mathrm{P}\left(\mathrm{A}\cap \mathrm{B}\right)}{\mathrm{P}\left(\mathrm{B}\right)} \\ P\left(\frac{B}{A}\right)=\frac{\left(\frac{15}{100}\right)}{\left(\frac{40}{100}\right)} \\ P\left(\frac{B}{A}\right)=\frac{15}{40} \\ P\left(\frac{B}{A}\right)=\frac{3}{8} \end{gathered}$$

Hence, the correct option is C.