In a group of people,
percent 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?
Select an Answer
View Correct Answer
The correct answer is A.
One way to determine the probability that neither person selected will have brown eyes is to count both the number of ways to choose two people at random from the people who do not have brown eyes and the number of ways to choose two people at random from all people, and then compute the ratio of those two numbers.
Since percent of the
people have brown eyes, there are
people with brown eyes, and
people who do not have brown eyes. The number of ways of choosing two people, neither of whom has brown eyes, is
: there are
ways to choose a first person and
ways to choose a second person, but there are
ways in which that same pair of people could be chosen. Similarly, the number of ways of choosing two people at random from the
people is
. Therefore, the probability that neither of the two people selected has brown eyes is
.
Another way 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 people times the probability of choosing one of the people who does not have brown eyes at random from the
remaining people after one of the people who does not have brown eyes has been chosen.
Since percent of the
people have brown eyes, the probability of choosing one of the people who does not have brown eyes at random from the
people is
. If one of the people who does not have brown eyes has been chosen, there remain
people who do not have brown eyes out of a total of
people; the probability of choosing one of the
people who does not have brown eyes at random from the
people is
. Therefore, if two people are to be selected from the group at random, the probability that neither person selected will have brown eyes is
.