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## Homework Statement

Four players play a board game which requires them to take it in turns to throw two fair dice. Each player throws the two dice once in each round. When a double is thrown the player moves forward six squares. Otherwise the player moves forward one square

## Homework Equations

Find:

a) the probability that the first double occurs on the third throw of the game

b) the probability that exactly one of the four players obtains a double in the first round

c) the probability that a double occurs exactly once in 4 of the first 5 rounds

## The Attempt at a Solution

a) A geometric problem.

[itex] \mathbb{P}\left ( X=3 \right )=\frac{1}{6}\left ( \frac{5}{6} \right )^{2}=0.1157 [/itex]

b) A binomial problem.

[itex] \mathbb{P}\left ( X=1 \right )=\binom{4}{1}\frac{1}{6}\left ( \frac{5}{6} \right )^{3}=0.3858 [/itex]

I've checked the answers for part a) and b) and they're correct.

c) This part i have no idea. I've wracked my brains for ages and i can't get clear about making sense of 'once in 4

of the first 5 rounds'. Any help would be brilliant