NCERT Class XI Mathematics - Probability - Solutions
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Question : 19
Total: 54
An experiment involves rolling a pair of dice and recording the numbers
that come up. Describe the following events:
A : the sum is greater than 8.
B : 2 occurs on either die.
C : the sum is at least 7 and a multiple of 3.
Which pairs of these events are mutually exclusive?
that come up. Describe the following events:
A : the sum is greater than 8.
B : 2 occurs on either die.
C : the sum is at least 7 and a multiple of 3.
Which pairs of these events are mutually exclusive?
Solution:
An experiment consists of rolling a pair of dice.
∴ Sample space consists 6 × 6 = 62 =36 possible outcomes.
S = {(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)}
Now, A : the sum is greater than 8
= {(3, 6), (4, 5), (4, 6), (5, 4), (5, 5), (5, 6), (6, 3), (6, 4), (6, 5), (6, 6)} B : 2 occurs on either die
= {(1, 2), (2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6), (3, 2), (4, 2), (5, 2), (6, 2)} C : The sum is at least 7 and a multiple of 3
= {(3, 6), (4, 5), (5, 4), (6, 3), (6, 6)}
A ∩ B = f, B ∩ C = ϕ
Thus above shows that A and B; B and C are mutually exclusive events
∴ Sample space consists 6 × 6 = 62 =36 possible outcomes.
S = {(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)}
Now, A : the sum is greater than 8
= {(3, 6), (4, 5), (4, 6), (5, 4), (5, 5), (5, 6), (6, 3), (6, 4), (6, 5), (6, 6)} B : 2 occurs on either die
= {(1, 2), (2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6), (3, 2), (4, 2), (5, 2), (6, 2)} C : The sum is at least 7 and a multiple of 3
= {(3, 6), (4, 5), (5, 4), (6, 3), (6, 6)}
A ∩ B = f, B ∩ C = ϕ
Thus above shows that A and B; B and C are mutually exclusive events
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