Question

$60$ percent people in a group of $10$ people, have brown eyes. Two people are to be selected at random from the group. What is the probability that neither person selected will have brown eyes?

• A. $0.13$
• B. $0.18$
• C. $0.25$
• D. $0.36$

Answer 1

The correct option is A $0.13$

To determine the probability that neither person selected will have brown eyes is to multiply the probability of choosing one of the people who does not have brown eyes at random from the $10$ people times the probability of choosing one of the people who does not have brown eyes at random from the $9$ remaining people after one of the people who does not have brown eyes has been chosen.

Since $60\%$ of the $10$ people have brown eyes, the probability of choosing one of the people who does not have brown eyes at random from the 10 people is $1-\frac{60}{100}=0.40$.

If one of the people who does not have brown eyes has been chosen, there remain $3$ people who do not have brown eyes out of a total of $9$ people; the probability of choosing one of the $3$ people who does not have brown eyes at random from the $9$ people is $\frac{3}{9}$.

Therefore, if two people are to be selected from the group at random, the probability that neither person selected will have brown eyes is $\frac{3}{9}\times 0.40\approx 0.13$