A number cube is rolled three times. What is the probability of rolling a 5 at least once?
Getting "a 5 at least once" = one, two or three 5s.
Once = 1/6(5/6)(5/6) = ?
Twice = 1/6(1/6)(5/6) = ?
Three times = 1/6^3 = ?
Either-or probabilities are found by adding individual probabilities.
To find the probability of rolling a 5 at least once when a number cube is rolled three times, we can use the concept of complementary probability.
The complementary probability is the probability of the event not happening. In this case, the complementary event is rolling a 5 no times, i.e., rolling a number other than 5 in all three rolls.
The probability of rolling a number other than 5 in one roll is 5/6 since there are six possible outcomes for each roll and only one of them is a 5.
To find the probability of rolling a number other than 5 in all three rolls, we multiply the probabilities together:
(5/6) * (5/6) * (5/6) = 125/216
The complementary probability is 125/216.
Now, to find the probability of rolling a 5 at least once, we subtract the complementary probability from 1:
1 - 125/216 = 91/216
Therefore, the probability of rolling a 5 at least once when a number cube is rolled three times is 91/216.
To find the probability of rolling a 5 at least once when a number cube is rolled three times, we need to find the probability of the complement event and subtract it from 1. The complement event is the event of not rolling a 5 in any of the three rolls.
The probability of not rolling a 5 on one roll is 5/6, since there are 5 numbers (1, 2, 3, 4, and 6) that are not 5, out of a total of 6 possible outcomes on the number cube.
To find the probability of the complement event (not rolling a 5 in any of the three rolls), we multiply the probabilities of not rolling a 5 on each individual roll. So, the probability of the complement event is (5/6) * (5/6) * (5/6).
Therefore, the probability of rolling a 5 at least once is:
1 - probability of the complement event
= 1 - (5/6) * (5/6) * (5/6)
= 1 - 125/216
= 91/216
So, the probability of rolling a 5 at least once when a number cube is rolled three times is 91/216.