Second roll beats the first

You roll a fair $6$ -sided die twice. What is the probability that the first roll is strictly less than the second?

Show hints (2)+

Of $36$ ordered outcomes, how many are ties? Split the rest by symmetry.
$6$ ties leave $30$ split evenly: $15$ each, so $\tfrac{15}{36}=\tfrac{5}{12}$ .

Answer

Reveal answer →

0.4167 (± 0.005)

Create a free account to see the full worked solution and track your progress.