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Probability — Maths STD 10 — Question

CBSE BoardEnglish MediumSTD 10MathsProbability5 Marks
Question
Two different dice are rolled simultanceously. Find the probability that the sum of the numbers on the two dice is 10.
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Answer

If two dice are rolled together, the possible outcomes are:
(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6)
(2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6)
(3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6)
(4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6)
(5, 1), (5, 2), (5, 3), (5, 4), (5, 5), (5, 6)
(6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6)
So, there are 36 outcomes.
The following outcomes will give sum of numbers on the two di ce to be 10:
(2, 5), (5, 2) and (5, 5)
So, there are 3 possible outcomes.
P(getting numbers whose sum is 10)
$=\frac{3}{36}$
$=\frac{1}{12}$

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