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Mathematics · 2025 · 3 marks
CBSE 2025 · Region 6 · Set 2 · Q31
A coin is biased so that the head is 3 times as likely to occur as tail. If the coin is tossed three times, find the probability distribution of…
A coin is biased so that the head is $\displaystyle 3$ times as likely to occur as tail. If the coin is tossed three times, find the probability distribution of number of tails. Hence, find the mean of the distribution.
Marking-scheme solution
\[\mathrm{P}(\mathrm{H})=\frac{3}{4}, \mathrm{P}(\mathrm{~T})=\frac{1}{4}
\]
| X | $\displaystyle 0$ | $\displaystyle 1$ | $\displaystyle 2$ | $\displaystyle 3$ |
| $\displaystyle \mathrm{P}(\mathrm{X})$ | $\displaystyle \frac{27}{64}$ | $\displaystyle \frac{27}{64}$ | $\displaystyle \frac{9}{64}$ | $\displaystyle \frac{1}{64}$ |
| $\displaystyle \mathrm{XP}(\mathrm{X})$ | $\displaystyle 0$ | $\displaystyle \frac{27}{64}$ | $\displaystyle \frac{18}{64}$ | $\displaystyle \frac{3}{64}$ |
| Mean $\displaystyle =\frac{3}{4}$ |
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CBSE Class 12 Mathematics past-paper question from the 2025 board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.