In a board game you may start only after rolling at least one six with two fair dice. What is the probability of getting at least one six on a single roll of the two dice?

\frac{1}{36}

Correct answerYour answer

\frac{1}{6}

Correct answerYour answer

\frac{5}{18}

Correct answerYour answer

\frac{11}{36}

Correct answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer D

Correct answer: D

No six on either die: $5 \times 5 = 25$ of the 36 outcomes.
P(at least one six) $= 1 - \frac{25}{36} = \frac{11}{36}$ .

Worth noting

$\frac{5}{18} = \frac{10}{36}$ is P(exactly one six), which leaves out the double six. $\frac{1}{6}$ is for one die only, and $\frac{1}{36}$ is P(two sixes).

Concept: 'At least one' with two dice
Typical timeTypical: 70 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.

In a board game you may start only after rolling at least one six with two fair dice. What is the probability of getting at least one six on a single roll of the two dice?

Explanation