JEE Main 2025 Jan 22 Shift 1, Mathematics Q6: Binomial Trials And Binomial Distribution

JEE Main2025Jan 22, Shift 1Mathematics

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 :

A
51
B
48
C
32
D
64

Solution

Counting HT patterns in each of the 8 equally-likely outcomes of three tosses:

HHH $\to$ 0, HHT $\to$ 1, HTH $\to$ 1, HTT $\to$ 1, THH $\to$ 0, THT $\to$ 1, TTH $\to$ 0, TTT $\to$ 0. So four outcomes give $X = 0$ and four give $X = 1$ .

Thus $P (X = 0) = 1/2$ , $P (X = 1) = 1/2$ (Bernoulli).

$μ = \frac{1}{2}$ ; $E [X^{2}] = \frac{1}{2}$ ; $σ^{2} = E [X^{2}] - μ^{2} = \frac{1}{2} - \frac{1}{4} = \frac{1}{4}$ .

$64 (μ + σ^{2}) = 64 (\frac{1}{2} + \frac{1}{4}) = 64 \cdot \frac{3}{4} = 48$ .

Concept behind this question

Binomial Trials And Binomial DistributionNotes, formulas and examples →

Practice more Mathematics

Concept-wise practice with instant solutions on Fundamenthol.

Start practicing →

JEE Main 2025 Jan 22 Shift 1, Mathematics Q6: Binomial Trials And Binomial Distribution

Concept behind this question

More previous year questions on Binomial Trials And Binomial Distribution

Practice more Mathematics