A coin is tossed three times. Let X denote the number of times a tail follows a head. If μ and σ 2 denote the mean and variance of X , then the value of 64 (μ+σ 2 ) is :

Mathematics · Probability

JEE Main 2025 — 22 January, Morning Shift — Question 6

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 :

Option A:
51
Option B:
48
Correct
Option C:
32
Option D:
64

Answer: B

Step-by-step solution

$\mathrm{HHH} \rightarrow 0$

HHT $\rightarrow 0$

HTH $\rightarrow 1$

HTT $\rightarrow 0$

THH $\rightarrow 1$

THT $\rightarrow 1$

TTH $\rightarrow 1$

TTT $\rightarrow 0$

Probability distribution

$\mu=\sum \mathrm{x}_{\mathrm{i}} \mathrm{p}_{\mathrm{i}}=\frac{1}{2}$

$\sigma^{2}=\sum x_{i}^{2} p_{i}-\mu^{2}$

$=\frac{1}{2}-\frac{1}{4}=\frac{1}{4}$

$64\left(\mu+\sigma^{2}\right)=64\left(\frac{1}{2}+\frac{1}{4}\right)=48$

Answer key and solution verified before publishing.

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Exam: JEE Main 2025
Paper: 22 January, Morning Shift
Subject: Mathematics
Chapter: Probability
Topic: Mean, variance, expected values of distributions

Two balls are selected at random one by one without replacement from a bag containing 4 white and 6 black balls. If the probability that…

Answer: B

Step-by-step solution

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