Question

# A pair of dice is thrown once. Find the probability of getting an even number on the first dice.

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Solution

## There are a total of $36$ possible outcomes. The following are the possible outcomes of a pair of dice thrown in sample space,{(1,1) , (1,2) , (1,3), (1,4), (1,5), (1,6), (2,1), (2,2), (2,3), (2,4), (2,5), (2,6), (3,1), (3,2), (3,3), (3,4), (3,5), (3,6), (4,1), (4,2), (4,3), (4,4), (4,5), (4,6), (5,1), (5,2), (5,3), (5,4), (5,5), (5,6), (6,1), (6,2), (6,3), (6,4), (6,5), (6,6)}Let $E$ denote the event of an even number on the first dice, and there are $18$ possible outcomes. The following are the favourable outcomes of event $E${(2,1), (2,2), (2,3), (2,4), (2,5), (2,6), (4,1), (4,2), (4,3), (4,4), (4,5), (4,6), (6,1), (6,2), (6,3), (6,4), (6,5), (6,6)}$ProbabilityofeventtohappenP\left(E\right)=\frac{Numberoffavourableoutcomes}{TotalNumberofoutcomes}$$⇒P\left(E\right)=\frac{n\left(E\right)}{n\left(S\right)}$$⇒P\left(E\right)=\frac{18}{36}=\frac{1}{2}$Therefore, Probability of getting an even number on the first dice $=\frac{1}{2}$

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