Q17. - Algebra 2

Question

There are 140 students in the school band. One of these students will be selected at random to be the student representative. If the probability that a brass player is selected is $\frac{\mathbf{2}}{\mathbf{5}}$, how many brass players are in the band?

Step-by-Step Solution

Answer

The number of brass players in the band is 56.

Step 1 ­- Description of step.

It is given that the number of students in the school band is 140 and the probability that a brass player is selected is $\frac{2}{5}$.

The probability of an event is given by:

$\text{Probability of an event = }\frac{\text{Number of favourable outcomes}}{\text{Total number of outcomes}}$.

Step 2 ­- Description of step.

Here, the favourable outcome is being the brass player.

Therefore, number of favourable outcomes is same as the number of brass players.

Total number of outcomes is same as the total number of students in school band.

Probability of an event is same as the probability of selection of brass player.

Therefore, it can be obtained that:

$\begin{array}{c}\text{Probability of selecting brass player = }\frac{\text{Number of brass players}}{\text{Total number of students in school band}}\\ \frac{2}{5}=\frac{\text{Number of brass players}}{140}\\ \frac{2}{5}\times 140=\text{Number of brass players}\\ 2\times 28=\text{Number of brass players}\\ 56=\text{Number of brass players}\end{array}$

Step 3 ­- Description of step.

Therefore, the number of brass players in the band is 56.