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Mathematics · 2025 · 2 marks
CBSE 2025 · Region 7 · Set 1 · Q25
(a) 10 identical blocks are marked with ' 0 ' on two of them, ' 1 ' on three of them, ' 2 ' on four of them and ' 3 ' on one of them and put in a…
(a)
$\displaystyle 10$ identical blocks are marked with ' $\displaystyle 0$ ' on two of them, ' $\displaystyle 1$ ' on three of them, ' $\displaystyle 2$ ' on four of them and ' $\displaystyle 3$ ' on one of them and put in a box. If X denotes the number written on the block, then write the probability distribution of X and calculate its mean.
OR
(b)
In a village of $\displaystyle 8000$ people, $\displaystyle 3000$ go out of the village to work and $\displaystyle 4000$ are women. It is noted that $\displaystyle 30 \%$ of women go out of the village to work. What is the probability that a randomly chosen individual is either a woman or a person working outside the village ?
Marking-scheme solution
(a)
Probability distribution table is:
| $\displaystyle \mathbf{X}$ | $\displaystyle \mathbf{0}$ | $\displaystyle \mathbf{1}$ | $\displaystyle \mathbf{2}$ | $\displaystyle \mathbf{3}$ |
| $\displaystyle \mathbf{P}(\mathbf{X})$ | $\displaystyle \frac{\mathbf{2}}{\mathbf{1 0}}$ | $\displaystyle \frac{\mathbf{3}}{\mathbf{1 0}}$ | $\displaystyle \frac{\mathbf{4}}{\mathbf{1 0}}$ | $\displaystyle \frac{\mathbf{1}}{\mathbf{1 0}}$ |
Mean $\displaystyle =\mathbf{E}(\mathbf{X})=\sum \mathbf{p}_{\mathrm{i}} \mathbf{x}_{\mathrm{i}}=\mathbf{0} \cdot \frac{\mathbf{2}}{\mathbf{1 0}}+\mathbf{1} \cdot \frac{\mathbf{3}}{\mathbf{1 0}}+\mathbf{2} \cdot \frac{\mathbf{4}}{\mathbf{1 0}}+\mathbf{3} \cdot \frac{\mathbf{1}}{\mathbf{1 0}}=\frac{\mathbf{1 4}}{\mathbf{1 0}}=\frac{\mathbf{7}}{5}$ (or $\displaystyle 1.4$)
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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.