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प्रश्न
A pair of dice is thrown and the sum of the numbers appearing on the dice is observed to be 7. Find the probability that the number 5 has appeared on atleast one die.
उत्तर
Let E = event that 5 has appeared on atleast one die
∴ E = {(5, 1), (5, 2), (5, 3), (5, 4), (5, 5), (5, 6), (6, 5), (4, 5), (3, 5), (2, 5), (1, 5)}
Let F = event that sum of no. on die is 7.
∴ F = {(1, 6), (2, 5), (3, 4), (4, 3), (5, 2), (6, 1)}
E ∩ F = {(2, 5), (5, 2)}
∴ n(E ∩ F) = 2
Now, `P(E/F) = (P(E ∩ F))/(P(F)) = (n(E ∩ F))/(n(F)) = 2/6 = 1/3`
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