Question

If $65\%$ of the population have black eyes and the rest brown eyes, what is the probability that a person selected at random has brown eyes?

Answer 1

Step 1 Finding population having brown eyes:

The percentage of the population having black eyes is $65$.

The population has either brown eyes or black eyes.

So the percentage of the population having brown eyes $=100-65=35$.

Step 2 Finding the probability that a person selected at random has brown eyes:

The formula for probability is

$Probability=\frac{Numberoffavorableoutcomes}{Totalnumberofoutcomes}$

Here, the number of favorable outcomes is $35$.

The total number of outcomes is $100$.

$$\begin{gathered} \Rightarrow P(browneyes)=\frac{35}{100} \\ \therefore P(browneyes)=\frac{7}{20} \end{gathered}$$

Hence, the probability that a person selected at random has brown eyes is $\frac{7}{20}$.