Final Answer:
The probability that a 5 is obtained on at least one of the rolls is approximately 0.598.
Step-by-step explanation:
To find the probability that a 5 is rolled at least once when a fair die is rolled 5 times, we use the concept of complementary events. The complement of getting at least one 5 is the event of not getting a 5 in any of the rolls.
A fair die has six sides, so the probability of rolling a 5 on any given roll is 1/6, while the probability of not rolling a 5 is 5/6.
Since the die rolls are independent, the probability of not rolling a 5 in all 5 rolls is the product of the probabilities of not rolling a 5 on each individual roll:
(5/6) * (5/6) * (5/6) * (5/6) * (5/6)
This can be simplified as:
(5/6)^5
Calculating this value gives the probability of not rolling a 5 at all in 5 rolls, which is roughly 0.402.
Now, to find the probability of the complementary event—rolling at least one 5—we subtract this probability from 1:
1 - 0.402 = 0.598
Thus, the probability of rolling at least one 5 when rolling a fair die 5 times is approximately 0.598 when rounded to three decimal places.