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Question

A dice is thrown two times and the sum of the scores appearing on the dice is observed to be a multiple of 4. Then the conditional probability that the score 4 has appeared atleast once is

A
13
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B
14
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C
18
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D
19
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Solution

The correct option is D 19
A: Sum obtained is a multiple of 4.
A={(1,3),(3,1), (2,6),(6,2), (3,5),(5,3), (2,2),(4,4),(6,6)}

B: Score of 4 has appeared at least once.
​​B={(1,4),(2,4),(3,4),(4,4),(5,4),(6,4), (4,1),(4,2),(4,3),(4,5),(4,6)}

From A and B,
(AB)=(4,4), n(AB)=1

Required probability =P(BA)=P (AB)P (A)=136936=19

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