# In order to decide who will play ﬁrst in a certain board game, each player rolls a four-sided die. Find the probability of obtaining at least one ‘triple four’ in four

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### 1 Answer

Each player rolls a four-sided die which is marked 1, 2, 3 and 4 on the four sides.

Each die can turn up any of the four numbers. The probability of a four turning up when a die is rolled is 1/4 and the probability that this does not happen is 3/4. There are C(4,3) ways of choosing the dice that turn up four. The last one does not. Using this, the required probability is: C(4,3)*(1/4)^3*(3/4) = 3/64

**The probability that a triple four turns up is 3/64**