two boys and three girls are auditioning to play the piano for a school production. two students will be…

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%

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

Explanation:

Step1: Calculate total number of students

There are 2 boys and 3 girls, so total students = 2 + 3=5.

Step2: Calculate probability of choosing a boy first

The probability of choosing a boy as the pianist first is $\frac{2}{5}$ since there are 2 boys out of 5 students.

Step3: Calculate probability of choosing a girl second

After choosing a boy first, there are 4 students left and 3 girls. So the probability of choosing a girl as the alternate is $\frac{3}{4}$.

Step4: Calculate combined probability

The probability that the pianist is a boy and the alternate is a girl is $\frac{2}{5}\times\frac{3}{4}=\frac{6}{20} = 0.3$.

Step5: Convert to percentage

To convert 0.3 to a percentage, we multiply by 100. So $0.3\times100 = 30%$.

Answer:

30%