Exam

JEE Main

Year

2025

Date

22 January

Shift

Morning Shift

Subject

Mathematics

Chapter

Probability

JEE Main 2025 · 22 January · Morning Shift · Mathematics · Probability

A coin is tossed three times. Let X denote the number of times a...

A coin is tossed three times. Let $X$ denote the number of times a tail follows a head. If $\mu and$\sigma^2$denote the mean and variance of$X$, then the value of$64$\left(\mu+\sigma^2\right)$ is :

Step-by-step solution

$$\begin{aligned} & \mu=\sum x_i P_i=\frac{1}{2} \\ & \sigma^2=\sum x_i^2 P_i-\mu^2 \\ & =\frac{1}{2}-\frac{1}{4}=\frac{1}{4} \\ & 64\left(\mu+\sigma^2\right)=64\left[\frac{1}{2}+\frac{1}{4}\right] \\ & =64 \times \frac{3}{4}=48\end{aligned}$$