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Probability — Maths STD 10 — Question

Gujarat BoardEnglish MediumSTD 10MathsProbability3 Marks
Question
  1. Two dice, one blue and one grey, are thrown at the same time. Complete the following table:
    Event: Sum on $2$ dice $2$ $3$ $4$ $5$ $6$ $7$ $8$ $9$ $10$ $11$ $12$
    Probability $\frac{1}{{36}}$           $\frac{5}{{36}}$       $\frac{1}{{36}}$
  2. A student argues that there are $11$ possible outcomes $2, 3, 4, 5, 6, 7, 8, 9, 10, 11$ and $12.$ Therefore, each of them has a probability $\frac{1}{11}$. Do you agree with this argument? Justify your answer.
✓

Answer

  1. It can be observed that,
    To get the sum as $2,$ possible outcomes $= (1, 1)$
    To get the sum as $3,$ possible outcomes $= (2, 1)$ and $(1, 2)$
    To get the sum as $4,$ possible outcomes $= (3, 1), (1, 3), (2, 2)$
    To get the sum as $5,$ possible outcomes $= (4, 1), (1, 4), (2, 3), (3, 2)$
    To get the sum as $6,$ possible outcomes $= (5, 1), (1, 5), (2, 4), (4, 2), (3, 3)$
    To get the sum as $7,$ possible outcomes $= (6, 1), (1, 6), (2, 5), (5, 2), (3, 4), (4, 3)$
    To get the sum as $8,$ possible outcomes $= (6, 2), (2, 6), (3, 5), (5, 3), (4, 4)$
    To get the sum as $9,$ possible outcomes $= (3, 6), (6, 3), (4, 5), (5, 4)$
    To get the sum as $10,$ possible outcomes $= (4, 6), (6, 4), (5, 5)$
    To get the sum as $11,$ possible outcomes $= (5, 6), (6, 5)$
    To get the sum as $12,$ possible outcomes $= (6, 6)$
    Event $2$ $3$ $4$ $5$ $6$ $7$ $8$ $9$ $10$ $11$ $12$
    Probability $\frac{1}{{36}}$ $\frac{2}{{36}}$ $\frac{3}{{36}}$ $\frac{4}{{36}}$ $\frac{5}{{36}}$ $\frac{6}{{36}}$ $\frac{5}{{36}}$ $\frac{4}{{36}}$ $\frac{3}{{36}}$ $\frac{2}{{36}}$ $\frac{1}{{36}}$
  2. The probability of each of these sums will not be $\frac{1}{11}$ as their sums are not equally likely.

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