Project ForgeTwo people, P and Q, decide to independently roll two identical dice, each with 6 faces, numbered 1 to 6. The person with the lower number wins. In case of a tie, they roll the dice repeatedly until there is no tie. Define a trial as a throw of the dice by P and Q. Assume that all 6 numbers on each die are equi-probable and that all trials are independent. The probability (rounded to 3 decimal places) that one of them wins on the third trial is ____.
Explanation
P(tie on a single trial) = 6/36 = 1/6. For the game to be decided on exactly the third trial, the first two trials must both be ties, and the third must NOT be a tie: P = (1/6)² × (5/6) = 5/216 ≈ 0.0231.
Source: GATE CS 2018 (2018)
This question is part of a 15-day revision cycle — sign in and Project Forge will bring it back the day before you'd forget it.