# 409 probability/icos.p

## Description

This article is from the Puzzles FAQ,
by Chris Cole chris@questrel.questrel.com and Matthew Daly
mwdaly@pobox.com with numerous contributions by others.

# 409 probability/icos.p

The "house" rolls two 20-sided dice and the "player" rolls one

20-sided die. If the player rolls a number on his die between the

two numbers the house rolled, then the player wins. Otherwise, the

house wins (including ties). What are the probabilities of the player

winning?

probability/icos.s

It is easily seen that if any two of the three dice agree that the

house wins. The probability that this does not happen is 19*18/(20*20).

If the three numbers are different, the probability of winning is 1/3.

So the chance of winning is 19*18/(20*20*3) = 3*19/200 = 57/200.

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