# What is the probability of rolling at least one "1" if you roll a six-sided dice six times?

##### 1 Answer

Feb 21, 2018

The answer is 0.665.

#### Explanation:

The probability of rolling at least one "1" if you roll a dice six times is the same as 1 minus the probability of rolling zero 1s if you roll a dice six times.

The probability of not rolling a 1 if you roll a dice once is 5/6. The probability of not rolling a 1 if you a roll a dice twice is 5/6 * 5/6. And so on... the probability of not rolling a 1 if you roll a dice six times is 5/6 * 5/6 * 5/6 * 5/6 * 5/6 * 5/6 * 5/6. Another way to write this is (5/6)^6. The answer here is 0.335.

So, the probability of rolling at least one 1 in six rolls of a dice is 1-0.335=0.665.