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Probability — Maths STD 10 — Question

CBSE BoardEnglish MediumSTD 10MathsProbability3 Marks
Question
Two dice, one blue and one grey are thrown at the same time. Write down all the possible outcomes. What is the probability that the sum of the two numbers appearing on the top of the dice is
  1. 8?
  2. 13?
  3. less than or equal to 12?
✓

Answer

When the blue die shows ‘1’, the grey die could show any one of the numbers 1, 2, 3, 4, 5, 6. The same is true when the blue die shows ‘2’, ‘3’, ‘4’, ‘5’ or ‘6’. The possible outcomes of the experiment are listed in the table below; the first number in each ordered pair is the number appearing on the blue die and the second number is that on the grey die.

So, the number of possible outcomes = 6 × 6 = 36.
  1. The outcomes favourable to the event ‘the sum of the two numbers is 8’ denoted by E, are: (2, 6), (3, 5), (4, 4), (5, 3), (6, 2) (see Fig.)
    i.e., the number of outcomes favourable to E = 5.
    Hence, P(E) = $\frac{5}{36}$
  2. As you can see from Fig., there is no outcome favourable to the event F, ‘the sum of two numbers is 13’.
    So, $P(F) = \frac{0}{36} = 0$
  3. As you can see from Fig., all the outcomes are favourable to the event G, ‘sum of two numbers ≤ 12’.
    So, P(G) = $\frac{36}{36}=1$

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