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Subject Test Math 2

Question 24 of 28

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SAT Subject Test

In a group of 10 people, 60 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?

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0.13

Correct Answer: 
Yes

0.16

Correct Answer: 
No

0.25

Correct Answer: 
No

0.36

Correct Answer: 
No

0.64

Correct Answer: 
No

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 10 people, and then compute the ratio of those two numbers.

Since 60 percent of the 10 people have brown eyes, there are 0.60 left parenthesis 10 right parenthesis equals 6 people with brown eyes, and 10 minus 6 equals 4 people who do not have brown eyes. The number of ways of choosing two people, neither of whom has brown eyes, is fraction numerator 4 left parenthesis 3 right parenthesis over denominator 2 end fraction equals 6: there are 4 ways to choose a first person and 3 ways to choose a second person, but there are 2 ways in which that same pair of people could be chosen. Similarly, the number of ways of choosing two people at random from the 10 people is fraction numerator 10 left parenthesis 9 right parenthesis over denominator 2 end fraction equals 45. Therefore, the probability that neither of the two people selected has brown eyes is fraction numerator 6 over denominator 45 end fraction almost equal to 0.13 invisible times.

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 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 percent 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 minus 0.60 equals 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 fraction numerator 3 over denominator 9 end fraction. Therefore, if two people are to be selected from the group at random, the probability that neither person selected will have brown eyes is 0.40 left parenthesis fraction numerator 3 over denominator 9 end fraction right parenthesis almost equal to 0.13.

Question Difficulty: 
hard