Two people, P and Q, decide to independently roll two identical dice, each…
2018
Two 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 dice 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 _____.
Attempted by 65 students.
Show answer & explanation
Correct answer: 0.021 to 0.024
Key idea: a trial is a tie if both players roll the same number. We need two consecutive ties followed by a decisive (non-tie) third trial.
Probability of a tie in one trial = 6/36 = 1/6.
Probability of a non-tie (decisive) trial = 1 - 1/6 = 5/6.
Probability that first two trials are ties and the third is decisive = (1/6) × (1/6) × (5/6) = 5/216 ≈ 0.023148...
Final answer (rounded to 3 decimal places): 0.023