JEE Main · 2019 · 10 Jan 2019 · Shift 1 · 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, \dots\dots, 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) $\frac{19}{72}$ ✓ Correct
(D) $\frac{19}{36}$

Answer: (C)

Solution

Split on the coin. On heads, two dice are thrown: a sum of

7

arises

6

ways and a sum of

8

arises

5

ways, so

11

36

outcomes work, a probability

\frac{11}{36}

. On tails, one of nine numbered cards is drawn and

7

8

2

9

, a probability

\frac{2}{9}

. Weighting each branch by the fair coin's

\frac{1}{2}

, the total is

\frac{1}{2} \cdot \frac{11}{36} + \frac{1}{2} \cdot \frac{2}{9} = \frac{11}{72} + \frac{8}{72} = \frac{19}{72}

JEE Main · 2019 · 10 Jan 2019 · Shift 1 · Single correct option

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JEE Main · 2019 · 10 Jan 2019 · Shift 1 · Probability

Solution

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