The standard deviation of the number of tails in three tosses of a coin is:
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → \(\displaystyle\frac{\sqrt{3}}{2}\)
The number of tails X in 3 tosses follows a binomial distribution with n = 3 and \(p = q = \frac{1}{2}\).
\( \displaystyle \text{Variance} = npq = 3 \times \frac{1}{2} \times \frac{1}{2} = \frac{3}{4} \)
\( \displaystyle \text{Standard deviation} = \sqrt{\frac{3}{4}} = \frac{\sqrt{3}}{2} \)
Why the other options are incorrect
Option (1) \(\displaystyle\frac{3}{4}\) — Incorrect. This is the variance; the standard deviation is its square root.
Option (2) \(\displaystyle\frac{3}{2}\) — Incorrect. This is the mean, np.
Option (3) \(\displaystyle\frac{3}{\sqrt{2}}\) — Incorrect. It is about 2.12, more than \(\sqrt{3}/2 \approx 0.87\).
NCERT Exemplar:
Probability
