Harvard-MIT Basic
2019


Problem - 4482

Your math friend Steven rolls five fair icosahedral dice (each of which is labelled $1$, $2$, $\cdots$, $20$ on its sides). He conceals the results but tells you that at least half of 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 $20$?


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