An unbiased coin is tossed. If outcome is a head then a pair of unbiased dice is rolled and sum of n

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14.Probability

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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 the is noted. If the toss of the coin results in tail then a card from a well-shuffled pack of nine cards numbered $1, 2, 3,….., 9$ is randomly picked and the number on the card is noted. The probability that the noted number is either $7$ or $8$ is

A

$\frac{{13}}{{36}}$

B

$\frac{{15}}{{72}}$

C

$\frac{{19}}{{72}}$

D

$\frac{{19}}{{36}}$

(JEE MAIN-2019)

Solution

$\mathrm{P}(7 \text { or } 8)$

$=P(H) P(7 \text { or } 8)+P(T) P(7 \text { or } 8)$

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

Standard 11

Mathematics

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