MathDB

Your math friend Steven rolls five fair icosahedral dice (each of which is labelled

1,2, \dots,20

on its sides). He conceals the results but tells you that at least half the rolls are

20

. Suspicious, you examine the first two dice and find that they show

20

and

19

in that order. Assuming that Steven is truthful, what is the probability that all three remaining concealed dice show

20

Problem Statement