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Counting and Basic Probability · Question 62 of 65

Question 62

MediumOriginal question

Two fair dice, one red and one blue, are rolled. What is the probability that the two numbers differ by exactly 2?

\frac{2}{9}

Correct answerYour answer

\frac{1}{6}

Correct answerYour answer

\frac{1}{9}

Correct answerYour answer

\frac{5}{18}

Correct answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer A

Correct answer: A

Unordered pairs differing by 2: (1, 3), (2, 4), (3, 5), (4, 6).
Each can appear with either die higher, so there are 8 outcomes out of 36.
Probability $= \frac{8}{36} = \frac{2}{9}$ .

Worth noting

$\frac{1}{9}$ counts only 4 outcomes, forgetting that red 3, blue 1 differs from red 1, blue 3. $\frac{5}{18}$ is P(differ by exactly 1).

Concept: Counting both orders for two distinguishable dice
Typical timeTypical: 70 s
Your timeYours: —

The rule this testsCoins, dice and cards

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