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

Question

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 (A) (1/3) (B) (2/5) (C) (3/8) (D) (1/7)

Tardigrade Admin · Accepted Answer

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 = (3/3+18) = (3/21) = (1/7)

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

$\frac{1}{3}$

$\frac{2}{5}$

$\frac{3}{8}$

$\frac{1}{7}$

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 $= \frac{3}{3 + 18} = \frac{3}{21} = \frac{1}{7}$