GATE CE 2022 Set 2 — Question 49
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Engineering Mathematics → Probability → Binomial Distribution
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Question
A pair of six-faced dice is rolled thrice. The probability that the sum of the outcomes in each roll equals 4 in exactly two of the three attempts is ______.
(round off to three decimal places)
(round off to three decimal places)
Correct answer
0.018 to 0.02
Solution
1.First, find the probability of getting a sum of 4 in a single roll of two six-faced dice.
The possible outcomes for a sum of 4 are: .Total number of outcomes for two dice = .
Probability of success in one trial, .
Probability of failure, .
2.The dice are rolled thrice (). We want the probability of exactly two successes ().
Using the binomial distribution formula :.
3.Rounding to three decimal places, the probability is .
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