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

30% A

Explanation:

Answer 2

30% is the correct answer.

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}) * P(\text{girl as alternate})}`

Formula for probability of an event E is given as:

`P(E) = \frac{\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}) = (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}) = (3)/(4)`

So, the required probability is:

`\text{Required probability } = (2)/(5)* (3)/(4) = (3)/(10) = \bold{30\%}`