Question

Five coins whose faces are marked $2,3$ are tossed. The chance of obtaining a total of $12$ is

• A. $\frac{1}{32}$
• B. $\frac{1}{16}$
• C. $\frac{3}{16}$
• D. $\frac{5}{16}$

Answer 1

The correct option is D

$\frac{5}{16}$

An explanation for the correct option:

Step 1: Find the probability of success and failure.

We have been given five coins whose faces are marked $2,3$ are tossed.

We need to find the chance of obtaining a total of $12$.

The condition for getting the total of $12$ would be,

$2,2,2,3,3$

The probability of getting $2$ is,

$p=\frac{1}{2}$

and the probability of getting $3$ is,

$q=\frac{1}{2}$

Step 2: Using the binomial distribution formula find the required probability.

Here, $n=5,r=3$

So the required probability would be,

$$\begin{gathered} \Rightarrow P={}^{5}C_3\times {\left(\frac{1}{2}\right)}^3\times {\left(\frac{1}{2}\right)}^{5-3} \\ \Rightarrow P=\frac{5!}{3!(5-3)!}\times \frac{1}{8}\times \frac{1}{4} \\ \Rightarrow P=10\times \frac{1}{32} \\ \Rightarrow \mathit{P}\mathbf{=}\frac{\mathbf{5}}{\mathbf{16}} \end{gathered}$$

Therefore, option (D) is the correct answer.