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Question

A die is thrown twice and the sum of the numbers appearing is observed to be 9. What is the conditional probability that the number 4 has appeared at least once?

A
12
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B
23
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C
34
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D
None of these
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Solution

The correct option is A 12
Let A be the event of getting the sum 9 and B be the event of getting at least one 4.
Then A = {(3, 6), (4, 5), (5, 4), (6, 3)}
B = {(1, 4), (2, 4), (3, 4) (4, 4), (5, 4), (6, 4),}
(4, 1), (4, 2), (4, 3), (4, 5), (4, 6)}
then AB=(4,5)(5,4)
Required probability =P(BA)=P(AB)P(A)
=n(AB)n(A)=24=12

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