Throw a dice 4 times. What is the probability `6` be up at-least one time? First time I approach a probability question (:


Throw a dice 4 times. What is the probability 6 be up at-least one time?

Intuitively, I would say: $\frac{1}{6}\times4$.
I would explain as: If you throw one time, probability is $\frac{1}{6}$.
If you do it 4 times, then multiply by 4.
According to the answers I'm wrong.
Can you explain please? thanks in advance.

Consider the complement problem, there is a 5/6 probability of not rolling a six
for any given die, and since the four dice are independent, the probability of not rolling a six is (5/6)^4 = 5^4/6^4 = 625/1296. The probability of rolling at least one six is therefore
1 − 625/1296 = 671/1296 ≈ .517.
