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

Answer:

30% is the correct answer.

Step-by-step explanation:

Total number of boys = 2

Total number of girls = 3

Total number of students = 5

To find:

Probability that the pianist will be a boy and the alternate will be a girl?

Solution:

Here we have to make 2 choices.

1st choice has to be boy (pianist) and 2nd choice has to be girl (alternate).

$\bold{\text{Required probability }= P(\text{boy as pianist first}) \times P(\text{girl as alternate})}$

Formula for probability of an event E is given as:

$P(E) = \dfrac{\text{Number of favorable cases}}{\text {Total number of cases}}$

For $P(\text{boy as pianist})$, number of favorable cases are 2 (total number of boys).

Total number of cases = Total number of students i.e. 5

So, $P(\text{boy as pianist})$ is:

$P(\text{boy as pianist}) = \dfrac{2}{5}$

For $P(\text{girl as alternate})$, number of favorable cases are 3 (total number of girls).

Now, one boy is already chosen as pianist so Total number of cases = Total number of students left i.e. (5 - 1) = 4

$P(\text{girl as alternate}) = \dfrac{3}{4}$

So, the required probability is:

$\text{Required probability } = \dfrac{2}{5}\times \dfrac{3}{4} = \dfrac{3}{10} = \bold{30\%}$