Ten standard 6-sided dice are rolled. What is the probability that exactly one of the dice shows a 1? Express your answer as a decimal rounded to the nearest thousandth.
The probability of rolling a 1 is 1/6.
The probability of rolling anything but a 1 is 5/6.
You want one 1 and nine not 1s: (1/6) x (5/6)9.
Since there are ten different places the 1 could be rolled, you need to multiply the answer in the above line by10.
Therefore, the probability of exactly one die, out of ten, shows a 1 is: 10 x (1/6) x (5/6)9 = 10 x 1 953 125 / 60 466 176
= 19 531 250 / 60 466 176
= 0.323 (approximately)