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})}](https://tex.z-dn.net/?f=%5Cbold%7B%5Ctext%7BRequired%20probability%20%7D%3D%20P%28%5Ctext%7Bboy%20as%20pianist%20first%7D%29%20%5Ctimes%20P%28%5Ctext%7Bgirl%20as%20alternate%7D%29%7D)
Formula for probability of an event E is given as:
![P(E) = \dfrac{\text{Number of favorable cases}}{\text {Total number of cases}}](https://tex.z-dn.net/?f=P%28E%29%20%3D%20%5Cdfrac%7B%5Ctext%7BNumber%20of%20favorable%20cases%7D%7D%7B%5Ctext%20%7BTotal%20number%20of%20cases%7D%7D)
For
, number of favorable cases are 2 (total number of boys).
Total number of cases = Total number of students i.e. 5
So,
is:
![P(\text{boy as pianist}) = \dfrac{2}{5}](https://tex.z-dn.net/?f=P%28%5Ctext%7Bboy%20as%20pianist%7D%29%20%3D%20%5Cdfrac%7B2%7D%7B5%7D)
For
, 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}](https://tex.z-dn.net/?f=P%28%5Ctext%7Bgirl%20as%20alternate%7D%29%20%3D%20%5Cdfrac%7B3%7D%7B4%7D)
So, the required probability is:
![\text{Required probability } = \dfrac{2}{5}\times \dfrac{3}{4} = \dfrac{3}{10} = \bold{30\%}](https://tex.z-dn.net/?f=%5Ctext%7BRequired%20probability%20%7D%20%3D%20%5Cdfrac%7B2%7D%7B5%7D%5Ctimes%20%5Cdfrac%7B3%7D%7B4%7D%20%3D%20%5Cdfrac%7B3%7D%7B10%7D%20%3D%20%5Cbold%7B30%5C%25%7D)