11
QuizMultiple Choice

Probability with Combinations and Permutations

Question 11 • Fall 24 GMS Geometry: Concepts and Connections B

Two boys and three girls are auditioning to play the piano for a school production. Two students will be chosen, one as the pianist, the other as the alternate.What is the probability that the pianist will be a boy and the alternate will be a girl? Express your answer as a percent.

Answer
A
30%
B
40%
C
50%
D
60%

Explanation

There are 2 boys among the 5 students, so the probability that the pianist is a boy is 2/5. After choosing a boy, 4 students remain, including all 3 girls, so the probability that the alternate is a girl is 3/4. Multiply: (2/5)(3/4) = 6/20 = 30%. The correct choice is 30%.

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