[Math] The probability of rolling 4 dice and getting a 6.

Question

The probability of rolling 2 dice and getting a 6 on either one of the die or both is : 11/36 or about 0.305.

Also I calculate the probability of rolling 4 dice and getting a 6 on either one, two, three or all four dice is : 421/1296 or about 0.32.

Is that correct? I am just surprised to find both the probabilities so close together.

Thank you.

Answer 1

The probability of getting at least $1$ six when rolling four dice is

$$ 1-(5/6)^{4}=1-625/1296=671/1296\approx 0.518 $$