CBSE 2025 · Region 1 · Set 3 · Q27 · 3 marks
Two dice are rolled together. Find the probability of getting :(i)a multiple of $\displaystyle 2$ on one and a multiple of $\displaystyle 3$ on the other die.(ii)the product of two numbers on the top of the two dice is a perfect square number.
Two dice are rolled together. Find the probability of getting :
(i)
a multiple of $\displaystyle 2$ on one and a multiple of $\displaystyle 3$ on the other die.
(ii)
the product of two numbers on the top of the two dice is a perfect square number.
Marking-scheme solution
Total outcomes = $\displaystyle 36$
(i)
$\displaystyle (2, 3)$, $\displaystyle (2, 6)$, $\displaystyle (3, 2)$, $\displaystyle (3, 4)$, $\displaystyle (3, 6)$, $\displaystyle (4, 3)$, $\displaystyle (4, 6)$, $\displaystyle (6, 2)$, $\displaystyle (6, 3)$, $\displaystyle (6, 4)$, $\displaystyle (6, 6)$
Number of outcomes having multiple of $\displaystyle 2$ on one die and a multiple of $\displaystyle 3$ on other die = $\displaystyle 11$
Hence, \(\displaystyle \mathrm{P}(\mathrm{E})=\frac{11}{36}\)
(ii)
$\displaystyle (1, 1)$, $\displaystyle (2, 2)$, $\displaystyle (3, 3)$, $\displaystyle (1, 4)$, $\displaystyle (4, 1)$, $\displaystyle (4, 4)$, $\displaystyle (5, 5)$, $\displaystyle (6, 6)$
Number of outcomes having product of two numbers on the top of the dice is a perfect square number = $\displaystyle 8$
\(\displaystyle \mathrm{P}(\mathrm{E})=\frac{8}{36}\) or \(\displaystyle \frac{2}{9}\)
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CBSE Class 10 Mathematics past-paper question from the 2025board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.