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Mathematics · 2026 · 3 marks
CBSE 2026 · Region 2 · Set 1 · Q31
Two dice are thrown at the same time. Determine the probability that the (i) sum of the numbers on the two dice is 5, and (ii) difference of the…
Two dice are thrown at the same time. Determine the probability that the
(i)
sum of the numbers on the two dice is $\displaystyle 5$, and (ii) difference of the numbers on the two dice is $\displaystyle 3$ .
Marking-scheme solution
Total outcomes = $\displaystyle 36$
(i)
Number of outcomes with sum of the numbers on the two dice is \(\displaystyle 5=4\)
\(\displaystyle (1,4)(4,1)(2,3)(3,2)\)
\(\displaystyle \mathrm{P}(\) sum of the numbers on two dice is $\displaystyle 5$\(\displaystyle )=\frac{4}{36}\) or \(\displaystyle \frac{1}{9}\)
(ii)
Number of outcomes with difference of the numbers on the two dice is \(\displaystyle 3=6\)
$\displaystyle (1,4)$ \(\displaystyle (4,1)(5,2)(2,5)(6,3)(3,6)\)
\(\displaystyle \mathrm{P}(\) difference of the numbers on the two dice is $\displaystyle 3$\(\displaystyle )=\frac{6}{36}\) or \(\displaystyle \frac{1}{6}\)
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CBSE Class 10 Mathematics past-paper question from the 2026 board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.