Mohit rolls a fair die twice. What is the probability that the first number is greater than the second?

\frac{5}{6}

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\frac{1}{2}

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\frac{7}{12}

Correct answerYour answer

\frac{5}{12}

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CorrectNot quiteAnswer D

Correct answer: D

Of the 36 outcomes, 6 are doubles, where the numbers are equal.
The other 30 split evenly: in 15 the first is bigger, in 15 the second is bigger.
Probability $= \frac{15}{36} = \frac{5}{12}$ .

Worth noting

$\frac{1}{2}$ forgets the 6 ties. $\frac{7}{12}$ is P(first is greater than or equal to the second), and $\frac{5}{6}$ is P(the numbers differ).

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

Explanation