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  4. A pair of fair dice is tossed repeatedly until a sum of four or an odd sum appears. Then the probability that a sum of four appears first is

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Q. A pair of fair dice is tossed repeatedly until a sum of four or an odd sum appears. Then the probability that a sum of four appears first is

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Solution:

The number of result of pair of dice which sum of $4$ is $3$. The number of result of a pair of dice which odd sum is $18$.
The probability the sum $4$ appear before the odd sum is $ = \frac{3}{3+18} = \frac{3}{21} = \frac{1}{7}$