JEE PYQ: Probability Question 43
Question 43 - 2019 (10 Jan Shift 1)
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:
(1) $\frac{13}{36}$
(2) $\frac{15}{72}$
(3) $\frac{19}{72}$
(4) $\frac{19}{36}$
Show Answer
Answer: (3)
Solution
$P = \frac{1}{2} \times \frac{11}{36} + \frac{1}{2} \times \frac{2}{9} = \frac{11}{72} + \frac{8}{72} = \frac{19}{72}$.
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