JEE Main · 2020 · 03 Sep 2020 · Shift 1 · Probability

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A die is thrown two times and the sum of the scorers appearing on the die is observed to be a multiple of 4. Then the conditional probability that the score 4 has appeared atleast once is

(A) $\frac{1}{9}$ ✓ Correct
(B) $\frac{1}{3}$
(C) $\frac{1}{8}$
(D) $\frac{1}{4}$

Answer: (A)

Solution

The sums that are multiples of

4

are

4

8

and

12

, arising from

(1, 3), (2, 2), (3, 1)

, then

(2, 6), (3, 5), (4, 4), (5, 3), (6, 2)

, and finally

(6, 6)

-- nine outcomes in all. Of these, only

(4, 4)

shows a

4

. The conditional probability is therefore

\frac{1/36}{9/36} = \frac{1}{9}

JEE Main · 2020 · 03 Sep 2020 · Shift 1 · Single correct option

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