GATE CS 2018 Set 1 — Question 25
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Engineering Mathematics → Probability & Statistics → Discrete Distributions
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Question
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 _____.
Correct answer
0.021 to 0.024
Solution
In a single trial (one roll by P and one by Q), there are total outcomes.
A tie occurs if both roll the same number: . There are 6 such outcomes.
Probability of a tie in one trial, .
Probability of a win (someone winning) in one trial, .We want the probability that the first win occurs on the third trial. This means the first two trials must result in ties and the third trial must result in a win:
Calculating the value:
Rounding to 3 decimal places, we get 0.023.
A tie occurs if both roll the same number: . There are 6 such outcomes.
Probability of a tie in one trial, .
Probability of a win (someone winning) in one trial, .We want the probability that the first win occurs on the third trial. This means the first two trials must result in ties and the third trial must result in a win:
Calculating the value:
Rounding to 3 decimal places, we get 0.023.
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