# Chances of rolling a 1 on any two/three consecutive dice rolls

This might be a stupid question.

If I roll a 1d6, it has 1/6 changes of rolling a 1. What are the chances of rolling a 1 if I roll the 1d6 two or three times in a row? On either roll.

• Can you be more precise about what you mean? The probability of rolling 3d6 and showing one 1 is different than the probability of rolling 3d6 and showing two 1s is different than the probability of rolling 3d6 and showing three 1s. Likewise, it's different from rolling a d6 until a certain number of 1s are shown. Are you asking about one of these events or a different event? – Sycorax Sep 4 at 13:39
• This is a simplified version of a question with an important history, de Méré's Problem. – whuber Sep 4 at 15:01

If you roll one die, you have a chance of $$\frac{5}{6}$$ to not roll a one.
Die rolls are independent. Therefore, chances multiply: the chance of rolling no one on two rolls is $$\left(\frac{5}{6}\right)^2$$, on three rolls $$\left(\frac{5}{6}\right)^3$$.
$$1-\left(\frac{5}{6}\right)^k$$
for $$k\in\{2,3\}$$, the number of rolls.