The experiment is rolling a fair die 3 times. Compute the probability of at least one face showing a 6

Answer 1

The probability of at least one face showing 6 is equal to 1 minus probability of always getting 5 or below. In other words, the only way to fail the condition of at least one 6 is to roll 5 or below for ALL your rolls.

P denotes probability.

P(6) = 1-P(5 or below)

Probability of rolling 5 or below is given by probability of each number multiplied by 5 = 1/6 * 5 = 5/6

P(5 or below) = 5/6

We multiply 5/6 by itself 3 times as it's a joint probability of 3 rolls.

P(3 rolls of 5 or below) = (5/6) * (5/6) * (5/6) = (5/6)^3

Finally calculating probability of at least one 6 in 3 rolls:

P(at least one 6) = 1-P(3 rolls of 5 or below) = 1 - 0.58 = 0.42