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Question

An unbiased coin is tossed. If the outcome is head then a pair of unbiased dice is rolled and the sum of the numbers obtained on them is noted. If the toss of the coin results in tail then a card from a well shuffled pack of nine cards numbered 1,2,9 is randomly picked and the number on the card is noted. The probability that the noted number is either 7 or 8 is :

A
1936
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B
1972
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C
1572
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D
1336
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Solution

The correct option is B 1972
P(H)=12, P(T)=12
If outcome is head,
P(7 or 8 is the sum of two dice)=1136
If outcome is tail,
P(7 or 8 is the number on card)=29
Then the probability that the noted number is either 7 or 8 =12×1136+12×29
=1972

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