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11 votes
11 votes
A first grade class of nine girls and seven boys walks into class in alphabetical order (by last name). What is the probability that three boys are the first to enter the room?A. 0.15B. 0.10C. 0.06D. 0.05

User Sven Tiffe
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1 Answer

20 votes
20 votes

Since there are nine girls and seven boys, there are a total of 16 people entering the classroom.

The probability that a boy enters the classroom first is 7/16, because there are 7 boys out of the total 16 people entering.

The probability that a boy enters the classroom second after the first one was a boy is 6/15, because one person has already entered and it was a boy.

The probability that a boy enters the classroom third after the first two were boys is 5/14, because two people have already entered the classroom and they were boys.

The order in which the other people enter the classroom does not matter in this problem, so we will not consider it.

Since we've already deduced the probability of each even happening, the final probability will be


P=(7)/(16)\cdot(6)/(15)\cdot(5)/(14)=(210)/(3360)=0.625\approx0.06

Thus, the probability that three boys are the first to enter the room is 0.06.

User Kindjacket
by
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