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.

Throw a dice six times - are you certain to get at least one six?
The mean number of sixes in four throws is indeed $\frac 23$. But there are combinations with $2, 3 \text{ or } 4$ sixes, and these reduce the number with just one six (apply the same argument to six throws, where it is more intuitive).
If you get no sixes in four throws, there are $5$ possibilities for each throw, and therefore $5^4=625$ possibilities with no six out of the $6^4=1296$ possibilities in total. So you get the probability by taking the $1296-625 = 671$ possibilities which must include at least one six, out of the $1296$ possibilities altogether.
