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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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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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.