Verified Solution • 2025–26 Session moderate

QJEEM25Maa5ba: JEE Main 2025 Mathematics - Class 12 JEEM25Maa5ba Solution: A coin is tossed three times. Let denote the number of times a…

A coin is tossed three times. Let XX denote the number of times a tail follows a head. If μ\mu and σ2\sigma^2 denote the mean and variance of XX , then the value of 64(μ+σ2)64\left(\mu+\sigma^2\right) is:

Multiple Choice Options

  • A 64
  • B 32
  • C 51
  • D 48

Step-by-Step Verified Solution

Outcome xix_i pip_i
HHH 0 18\frac{1}{8}
TTT 0 18\frac{1}{8}
HHT 1 18\frac{1}{8}
HTH 1 18\frac{1}{8}
THH 0 18\frac{1}{8}
TTH 0 18\frac{1}{8}
THT 1 18\frac{1}{8}
HTT 1 18\frac{1}{8}
amp;μ=∑xiPi=12amp;σ2=∑xi2Pi−μ2amp;=12−14=14amp;64(μ+σ2)=64[12+14]amp;=64×34=48\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}

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