Question

A fair die is rolled 4 times. What is the probability that a 4 is obtained on at least one of the rolls? Round your answer to three decimal places.

Answer 1

The probability of rolling a 4 on at least one of the four rolls of a fair die is approximately 0.518.

Step-by-step explanation:

To find the probability of rolling a 4 on at least one of the four rolls of a fair die, we can use the concept of complementary events. The complementary event in this case is rolling a 4 on none of the rolls. The probability of rolling a 4 on any single roll is 1/6, so the probability of not rolling a 4 on any single roll is 5/6. Since the rolls are independent, we can multiply the probabilities together to find the probability of not rolling a 4 on any of the four rolls: (5/6)^4 = 625/1296. Therefore, the probability of rolling a 4 on at least one of the rolls is 1 - 625/1296 = 671/1296 ≈ 0.518.

Answer 2

Well, based on the scenario, we need to use this formula in order to find out the probability of getting 4

1 -
`(5^4)/(6^4)`

= 1 -
`(625)/(1296)`

=
`(671)/(1296)`

= 51.71 %