At a board-game club, two fair dice are rolled together. What is the probability that the total is a prime number?

\frac{1}{2}

Correct answerYour answer

\frac{5}{11}

Correct answerYour answer

\frac{5}{12}

Correct answerYour answer

\frac{7}{12}

Correct answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer C

Correct answer: C

Possible prime totals: 2, 3, 5, 7, 11.
Ways: 2 in 1 way, 3 in 2, 5 in 4, 7 in 6, 11 in 2, so $1 + 2 + 4 + 6 + 2 = 15$ .
Probability $= \frac{15}{36} = \frac{5}{12}$ .

Worth noting

$\frac{5}{11}$ counts 5 prime totals out of 11 possible totals, but the totals are not equally likely. $\frac{1}{2}$ is P(odd total), which includes 9 and leaves out 2. $\frac{7}{12}$ is P(not prime).

Concept: Weighting each dice total by its number of ways
Typical timeTypical: 70 s
Your timeYours: —

The rule this testsCoins, dice and cards

Practise this chapter →

Ten questions from Counting and Basic Probability, at your own pace.

At a board-game club, two fair dice are rolled together. What is the probability that the total is a prime number?

Explanation