Wrong result for Q15:"Max Dice Roll"

[LoicH]

Hi @adijo, I believe that in your PDF, the solution for question 15 "Max Dice Roll" is not the expected answer.

You write the formula for P(max{X1, ..., Xn} <= r) but we don't want the probability that the largest number rolled is less than (or equal to) r. We want the probability that the largest number rolled is equal to r.

So the expected result is P(max{X1, ..., Xn} = r) which changes the formula:

P(max{X1, ..., Xn} = r) = r^n/6^n - (r-1)^n/6^n
(from here)

You can verify that the PDF formula does not give the wanted result:

• for n=1 and r=2: "What is the probability that I roll a 2?" We know it's 1/6 but the formula gives 2/6.
• for r=6: "What is the probability that the largest number rolled is 6?". The formula gives a probability of 1, which means that whatever the number of rolls, we will get a 6! That would be nice!