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  • Three dice are thrown at the same time. Find the probability of getting three twos’, if it is known that the sum of the numbers on the dice was six.

Three dice are thrown at the same time. Find the probability of getting three twos’, if it is known that the sum of the numbers on the dice was six.

Answers (1)

Since three dice are thrown at the same time, the sample space is [n(S)] = 63= 216.

Let E1 be the event when the sum of numbers on the dice was six and

 E2 be the event when three twos occur.

\\ \Rightarrow \quad E_{1}=\{(1,1,4),(1,2,3),(1,3,2),(1,4,1),(2,1,3),(2,2,2,),(2,3,1),(3,1,2),(3,2,1),(4,1,1)\} \\ \Rightarrow n\left(E_{1}\right)=10 \text { and } E_{2}\{2,2,2\} \\ \Rightarrow n\left(E_{2}\right)=1 \\ \text { And }\left(E_{1} \cap E_{2}\right)=1 \\ P\left(E_{1}\right)=\frac{10}{216} \\ P\left(E_{1} \cap E_{2}\right)=\frac{1}{216} \\ \therefore P\left(E_{2} \mid E_{1}\right)=\frac{P\left(E_{1} \cap E_{2}\right)}{P\left(E_{1}\right)} \\ \frac{\frac{1}{216}}{\frac{10}{216}}=\frac{1}{10}

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