GATE ME 2018 Set 1 — Question 28
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Engineering Mathematics → Statistics & Distributions → Binomial Distribution
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Question
A six-faced fair dice is rolled five times. The probability (in %) of obtaining “ONE” at least four times is
Correct answer
(C) 0.33
Solution
This is a problem of binomial probability.
Let be the number of trials (rolls of the dice). Here, .
Let be the probability of success in a single trial, which is obtaining a “ONE”. For a fair six-faced dice, .
Let be the probability of failure, which is not obtaining a “ONE”. So, .The probability of getting exactly successes in trials is given by the binomial probability formula:We need to find the probability of obtaining “ONE” at least four times, which is .
Let be the number of trials (rolls of the dice). Here, .
Let be the probability of success in a single trial, which is obtaining a “ONE”. For a fair six-faced dice, .
Let be the probability of failure, which is not obtaining a “ONE”. So, .The probability of getting exactly successes in trials is given by the binomial probability formula:We need to find the probability of obtaining “ONE” at least four times, which is .
1.Probability of getting exactly 4 “ONE”s:
2.Probability of getting exactly 5 “ONE”s:
3.The total probability of getting at least four “ONE”s is the sum of these two probabilities:
To express this as a percentage, we multiply by 100:Comparing this result with the given options, the closest value is 0.33.Continue learning with Success Tracker
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