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

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Amiya Arellano

Answered question

2022-02-12

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

Answer & Explanation

Janessa Oneill

Beginner2022-02-13Added 10 answers

Step 1
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

\frac{5}{6}

.
The probability of not rolling a 1 if you a roll a dice twice is

\frac{5}{6} \times \frac{5}{6}

And so on... the probability of not rolling a 1 if you roll a dice six times is

\frac{5}{6} \times \frac{5}{6} \times \frac{5}{6} \times \frac{5}{6} \times \frac{5}{6} \times \frac{5}{6} \times \frac{5}{6}

Another way to write this is

{(\frac{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

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