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An unbiased coin is tossed. If the outcome is a head then a pair of unbiased dice is rolled and the sum of the numbers obtained on them is noted. lf the toss of the coin results in tail then a card from a well-shuffled pack of nine cards numbered 1, 2, 3, .... , 9 is randomly picked and the number on the card is noted. The probability that the noted number is either 7 or 8 is

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15/72

19/36

13/36

19/72

answer is C.

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Detailed Solution

When a pair of dice is rolled, then probability of sum of numbers obtained is 7 or 8 is 11/36. And the probability that a card numbered 7 or 8 came from a pack of cards numbered 1, 2, ... 9 is 2/9.

$∴ Required probability = \frac{1}{2} \times \frac{11}{36} + \frac{1}{2} \times \frac{2}{9} = \frac{19}{72}$

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