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प्रश्न
Given that the two numbers appearing on throwing two dice are different. Find the probability of the event 'the sum of numbers on the dice is 4'.
उत्तर
Consider the given events
A = Numbers appearing on two dice are different
B = The sum of the numbers on two dice is 4
Clearly,
A = {(1, 2), (1, 3), (1, 4), (1, 5), (1, 6),
(2, 1), (2, 3), (2, 4), (2, 5), (2, 6),
(3, 1), (3, 2), (3, 4), (3, 5), (3, 6)
(4, 1), (4, 2), (4, 3), (4, 5), (4, 6),
(5, 1), (5, 2), (5, 3), (5, 4), (5, 6),
(6, 1), (6, 2), (6, 3), (6, 4), (6, 5)}
B = {(1, 3), (3, 1) and (2, 2)}
\[\text{ Now } , \]
\[A \cap B = \left\{ \left( 1, 3 \right) \text{ and } \left( 3, 1 \right) \right\}\]
\[ \therefore \text{ Required probability } = P\left( B/A \right) = \frac{n\left( A \cap B \right)}{n\left( A \right)} = \frac{2}{30} = \frac{1}{15}\]
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