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.

Guest Dec 11, 2017

#1**+1 **

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)

geno3141 Dec 11, 2017