Change set

Pick exam & year, then Go.

Question map
Not attempted Correct Incorrect ★ Bookmarked
Loading…
Q20 (IAS/2007) Science & Technology › Basic Science (Physics, Chemistry, Biology) › Quantitative aptitude topics Answer Verified

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

Result
Your answer: —  Â·  Correct: C

Explanation

Each die has 6 faces, so the total number of ordered outcomes when three dice are rolled is 6^3 = 216 . To count outcomes in which no die shows a 2, each die then has 5 possible faces (1,3,4,5,6), giving 5^3 = 125 such outcomes [1]. By complement, the number of outcomes with at least one die showing a 2 equals total outcomes minus those with no 2, i.e., 216 − 125 = 91 [1]. Therefore the correct choice is the option corresponding to 91.

Sources

  1. [1] https://www.pdx.edu/student-academic-support-services/sites/learningcenter.web.wdt.pdx.edu/files/2020-07/Probability_Dice.pdf
How others answered
Each bar shows the % of students who chose that option. Green bar = correct answer, blue outline = your choice.
Community Performance
Out of everyone who attempted this question.
50%
got it right
✓ Thank you! We'll review this.

SIMILAR QUESTIONS

CAPF · 2012 · Q9 Relevance score: 4.30

Three dice, whose all six faces arc- marked ‘1’ to ‘6’, are thrown. The number of ways of getting a sum of 16 is

IAS · 2006 · Q103 Relevance score: 2.20

Each of the six faces of a cube is numbered by one of the six digits from 1 to 6. This cube is shown in its four different positions in the figures I, II, III and IV: Consider the following statements: I. Figures II and III are sufficient to know as to which face is opposite to the face numbered 6. II. Figure II and III are sufficient to know as to which face is opposite to the face numbered 4. III. Figures I and IV are sufficient to know as to which face is opposite to the face numbered 3. Which of the statements given are correct?

IAS · 1997 · Q137 Relevance score: -3.09

When three coins are tossed together, the probability that all coins have the same face up is:

A) 1/3
B) 1/6
C) 1/4
D) 1/8

CAPF · 2017 · Q116 Relevance score: -3.57

Two positions of a dice with 1 to 6 dots on its side are shown below : XTTFl XTTFI fr-. Fr- jj/ Liiy If the dice is resting on the side with three dots, what will be the number of dots on the side at the top ?