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Probability — Maths STD 10 — Question

Maharashtra BoardEnglish MediumSTD 10MathsProbability4 Marks
Question
Two dice, one blue and one grey, are thrown at the same time. Complete the following table:
Event 'Sum on two dice' 2 3 4 5 6 7 8 9 10 11 12
Probability                      
From the above table 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?
✓

Answer

Two dice (one blue and one green) are thrown at the same time
$\therefore$ Total number of outcomes (n) = 6 × 6 = 36
When sum of two dise = 2, then these will be (1, 1) = 1
When sum is 3, then (1, 2) (2, 1) = 2
When sum is 4, then (1, 3), (2, 2), (3, 1) = 3
When sum is 5, then (1, 4), (2, 3), (3, 2), (4, 1) = 4
When sum is 6, then (1, 5), (2, 4), (3, 3), (4, 2), (5, 1) = 5
When sum is 7, then (1, 6), (2, 5), (3, 4), (4, 3), (5, 2), (6, 1) = 6
When sum is 8, then (2, 6), (3, 5), (4, 4), (5, 3), (6, 2) = 5
When sum is 9, then (3, 6), (4, 5), (5, 4), (6, 2) = 4
When sum is 10, then (4, 6), (5, 5), (6, 4) = 3
When sum is 11, then (5, 6), (6, 5) = 2
When sum is 12, then (6, 6) = 1
Now we will complete the given table as below
Event' Sum on two dice' 2 3 4 5 6 7 8 9 10 11 12
Probability $\frac{1}{36}$ $\frac{2}{36}$ $\frac{3}{36}$ $\frac{4}{36}$ $\frac{5}{36}$ $\frac{6}{36}$ $\frac{5}{36}$ $\frac{4}{36}$ $\frac{3}{36}$ $\frac{2}{36}$ $\frac{1}{36}$
No, the outcomes are not equally likely.

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