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

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 as pianist

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

Step3: Calculate probability of choosing a girl as alternate after choosing a boy as pianist

After choosing a boy as the pianist, there are 4 students left, and 3 of them are 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 the product of the two probabilities above, $\frac{2}{5}\times\frac{3}{4}=\frac{6}{20} = 0.3$.

Step5: Convert to percentage

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

Answer:

30%