Question

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.

30%
40%
50%
60%

Answer 1

There are 5 choices for pianist and then 4 remaining for alternate, so 20 equally likely ordered pairs. Favorable pairs: choose a boy for pianist (2 ways) and a girl for alternate (3 ways) for 2·3 = 6 pairs. Probability = 6/20 = 3/10 = 30%.

Answer: 30%