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%

Explanation:

Step1: Calculate probability of choosing a boy first

There are 2 boys and 3 girls, so 5 students in total. The probability of choosing a boy as the pianist is $\frac{2}{5}$ since there are 2 boys out of 5 students.

Step2: Calculate probability of choosing a girl second

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

Step3: Calculate combined probability

The probability of both events happening is the product of their individual probabilities. So $P=\frac{2}{5}\times\frac{3}{4}=\frac{6}{20} = 0.3$.

Step4: Convert to percentage

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

Answer:

30%