UPSC Prelims 2007 · General Studies

Question 139: Basic Numeracy

Three dice (each having six faces with each face showing one number from 1 to 6) are rolled. What is the number of possible outcomes such that at least one die shows the number 2?

a36

b81

c91

d116

AnswerThe answer is (c).

Count all outcomes and subtract those with no 2. Three dice give 6^3 = 216 outcomes. Outcomes where no die shows 2 give 5^3 = 125. So the outcomes with at least one 2 are 216 - 125 = 91. Counting 'at least one' by subtracting the 'none' case is usually quicker.

Why each option is right or wrong

(a) 36 is far too small.
(b) 81 is too small; the count is 91.
(c) Correct: 216 - 125 = 91.
(d) 116 is too large.

Explanation: written by UPSC Grade, not by UPSC.

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Source: UPSC, Civil Services (Preliminary) Examination 2007, General Studies. UPSC's own paper isn't online; the words are from a published compilation. The paper on upsc.gov.in.