Given a die, what is the probability that the second roll of a die will be less than the first roll?

If you are given a die and asked to roll it twice. What is the probability that the value of the second roll will be less than the value of the first roll?

05-Sep-2015 2:01 PM

Answers (1)


There is 1/6 chance that both the rolls will be same. So, there's 5/6 chance that both rolls will be different

Now, for 2 rolls with different results, there can be 2 cases:

  • 1st roll result is greater
  • 2nd roll result is greater

We can see that the chances of these 2 cases will be equal ( = 1/2 ), eg. switch the 2 dice

So, answer = (5/6) x (1/2) = 5/12

05-09-2015 14:09

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