# Three four-sided (tetrahedral) dice are thrown together. Each dieis labelled with 1,2,3,4 on its four sides. Find the probability ofobtaining all fours.

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Three four-sided (tetrahedral) dice are thrown together. Each die

is labeled with 1,2,3,4 on its four sides. Of the four values the probability of a die turning up 4 is 1/4 = 0.25

The probability of all the four dice turning up 4 is (1/4)^4 = 1/256

**The required probability is 1/256.**

Three four-sided (tetrahedral) dice are thrown together. Each die

is labeled with 1,2,3,4 on its four sides. Of the four values the probability of a die turning up 4 is 1/4 = 0.25The probability of all the four dice turning up 4 is (1/4)^4 = 1/256

The required probability is 1/256.

Find the probability of obtaining at least one ‘triple four’ in four

tosses of the three dice. [6]

(b) In order to decide who will play ﬁrst in a certain board game, each

player rolls a four-sided die; the player with the highest score begins.

(i) What is the probability that two particular people obtain the

same score? [1]

(ii) Three people decide to play the game. What is the probability

that when they roll the die to decide who starts, they all obtain

diﬀerent scores?