A fair die is rolled seven times. What is the probability that it comes up 5 at least once? Write your answer as a fraction or a decimal, rounded to four decimal places.

Answer: 0.7209

Step-by-step explanation:

For a fair die, probability of occurrence of any face (including 5) = 1/6.

To determine the probability of having at least one * 5" in 7 rolls, the probability distribution formula for occurrence of random variables by combination method is used.

To determine no of occurrence "r" from a total occurrence "n", the probability formula is denoted by:

P (X=r) = nCr * p^r * q^n-r

Where p = probability of success which in this case = 1/6

q = 1-p = 1 - 1/6 = 5/6

To determine the probability of the occurrence of at least one occurrence of "5" from 7 throws, that is P (X≥1), we can determine the probability of occurrence of not having 5 at all and deduct our answer from 1. That is, P (X≥1) = 1 - P (X=0)

When r = 0,

P (X=0) = 7C0 * (1/6) ^0 * (5/6) ^7 = 0.2791

Hence, P (X≥1) = 1 - 0.2791 = 0.7209