SOLUTION: There are 9 students in a class: 7 boys and 2 girls. If the teacher picks a group of 3 at random, what is the probability that everyone in the group is a boy?

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Question 851271: There are 9 students in a class: 7 boys and 2 girls.
If the teacher picks a group of 3 at random, what is the probability that everyone in the group is a boy?
Found 3 solutions by ewatrrr, KOlszewski, ikleyn:
Answer by ewatrrr(24785)   (Show Source):
You can put this solution on YOUR website!

Hi,
9 students in a class: 7 boys and 2 girls.
picks a group of 3 at random
P(all boys) =

Answer by KOlszewski(2)   (Show Source):
You can put this solution on YOUR website!

Answer by ikleyn(52781)   (Show Source):
You can put this solution on YOUR website!
.

In this problem, the space of events is the set of all possible different groups of 3 persons that can be formed of 7+2 = 9 students. The number of such groups is = = 84. It is the number of events in the space of events. Of them, the favorable set is the set of all different groups that can be formed of 7 boys. The number of such groups is = = 35. The probability under the problem's question is the ratio of the numer of favorable events (35) to the number of all possible outcomes (84) P = = = 0.4167 = 41.67% (approximately). ANSWER

There is another way to get the SAME answer.

The probability that the first selected student is a boy is . If the first selected student is a boy, then the probability that the second selected student is a boy is . If the first and the second selected students are boys, then the probability that the third selected student is a boy is . Thus the probability under the problem's question is = 0.4167 = 41.67%.

Solved.