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  4. 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. 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 :

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Q. 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. 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 :

JEE MainJEE Main 2019Probability - Part 2

Solution:

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$P ( A )=\frac{1}{2} \times \frac{11}{36}+\frac{1}{2} \times \frac{2}{9}=\frac{19}{72}$