Two fair dice are rolled together. What is the probability that the numbers shown add up to 9?

\frac{1}{12}

Correct answerYour answer

\frac{1}{11}

Correct answerYour answer

\frac{2}{21}

Correct answerYour answer

\frac{1}{9}

Correct answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer D

Correct answer: D

There are $6 \times 6 = 36$ equally likely ordered outcomes.
Sum 9: (3, 6), (6, 3), (4, 5), (5, 4), which is 4 outcomes.
Probability $= \frac{4}{36} = \frac{1}{9}$ .

Worth noting

$\frac{1}{11}$ treats the 11 possible sums (2 to 12) as equally likely. $\frac{2}{21}$ counts unordered pairs, but (3, 6) and (6, 3) are different outcomes. $\frac{1}{12}$ misses one of the four.

Concept: Ordered outcomes for two dice
Typical timeTypical: 40 s
Your timeYours: —

The rule this testsCoins, dice and cards

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

Two fair dice are rolled together. What is the probability that the numbers shown add up to 9?

Explanation