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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.

Verified Answer :

Answer: The probability that he pianist will be a boy and the alternate will be a girl is 30%.

Explanation:

Since we have given that

Number of boys are auditioning to play the piano for a school production = 2

Number of girls are auditioning to play the piano for a school production = 3

Total number of candidates is given by

\(2+3=5\)

Now,

Let Event A denotes pianist will be a boy.

Let Event B denotes alternate will be girl.

Since Event A and B are independent events so,

\(P(\text{ A and B})=P(A)\times P(B)\)

So,

Probability that the pianist will be a boy and the alternate will be a girl is given by

\(\frac{2}{5}\times \frac{3}{4}\\\\=\frac{6}{20}=\frac{3}{10}\)

Now, we have to change it into percent ,

\(\frac{3}{10}\times 100=3\times 10=30\%\)

Hence ,the probability that he pianist will be a boy and the alternate will be a girl is 30%.

The probability helps us to know the chances of an event occurring. The probability that the pianist will be a boy and the alternate will be a girl is 0.3.

What is Probability?

The probability helps us to know the chances of an event occurring.

\(\rm Probability=\dfrac{Desired\ Outcomes}{Total\ Number\ of\ outcomes\ possible}\)

As there are 2 boys and 3 girls. And out of this total of 5 people, we need to know the probability of a boy being selected first. Therefore, the probability can be written as,

\(\rm Probability=\dfrac{Desired\ Outcomes}{Total\ Number\ of\ outcomes\ possible}\)

\(\rm Probability=\dfrac{\text{Number of boys}}{\text{Number of people}} = \dfrac{2}{5}\)

Now since one boy is already selected the number of choices will reduce to 4, therefore, the probability of selecting a girl next can be written as,

\(\rm Probability=\dfrac{Desired\ Outcomes}{Total\ Number\ of\ outcomes\ possible}\)

\(\rm Probability=\dfrac{\text{Number of girls}}{\text{Number of people}} = \dfrac{3}{4}\)

Thus, the probability that the pianist will be a boy and the alternate will be a girl can be written as,

\(\rm Probability=\dfrac25 \times \dfrac34 = \dfrac{3}{10} = 0.3\)

Hence, the probability that the pianist will be a boy and the alternate will be a girl is 0.3.

Learn more about Probability:

https://brainly.com/question/795909

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