A fair die is rolled 5 times. What is the probability that a 5 is obtained on at least one of the rolls?
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9$\begingroup$ Welcome to Mathematics Stack Exchange. Do you know what is the probability that no $5$ is obtained on any of the rolls? $\endgroup$– J. W. TannerCommented Dec 24, 2023 at 18:58
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$\begingroup$ The community rules suggest you should demonstrate an attempt to solution, please, write what you've tried and how $\endgroup$– Daigaku no BakuCommented Dec 24, 2023 at 19:05
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$\begingroup$ Virtually every posted question that I have seen on MathSE that followed this article on MathSE protocol, has generated a positive reaction among MathSE reviewers, who then enthusiastically attacked the problem for the original poster. $\endgroup$– user2661923Commented Dec 24, 2023 at 19:26
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1 Answer
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To find the probability of obtaining a 5 on at least one of the rolls of a fair six-sided die, you can use the complement rule. The complement of the event "getting a 5 on at least one roll" is the event "not getting a 5 on any of the rolls."
The probability of not getting a 5 on a single roll is 5/6 (since there are five outcomes (1, 2, 3, 4, 6) out of six that are not a 5).
Since each roll is independent, the probability of not getting a 5 on any of the five rolls is (5/6)^(5) (raising the probability of a single roll to the power of the number of rolls).
Now, to find the probability of getting a 5 on at least one roll, subtract the probability of not getting a 5 from 1:
P(at least one 5)=1−P(not getting a 5 on any roll)
P(at least one 5)=1−(5/6)^(5)
Calculating this expression will give you the probability of getting at least one 5 in 5 rolls of the fair die.
