Chapter 10.7, Problem 20STP

To determine

To find: The probability of students who would choose action film as their favourite type of film.

Answer to Problem 20STP

The option $H$ is correct.

Explanation of Solution

Given information: $27\mathrm{out}\mathrm{of}60$ students who would choose action film as their favourite type of film.

Calculation: $27\mathrm{out}\mathrm{of}60$ students who would choose action film as their favourite type of film.

In another group total students is $480$ .

Let students who would choose action film as their favourite type of film is $x$ .

Both group are similar so probability is same

  $\mathrm{P}(\mathrm{event})=\frac{\mathrm{number}\mathrm{of}\mathrm{favourable}\mathrm{outcomes}}{\mathrm{number}\mathrm{of}\mathrm{total}\mathrm{outcomes}}$

  $\begin{array}{l}\mathrm{P}(A)=\frac{27}{60}=\frac{9}{20}\\ P(B)=\frac{x}{480}\\ P(A)=P(B)\\ \frac{9}{20}=\frac{x}{480}\\ \mathrm{cross}\mathrm{multiply}\\ 9\times 480=20x\\ \frac{9\times 480}{20}=x\\ 9\times 24=x\\ 216=x\end{array}$

Thus, the option $H$ is correct.