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.

Use the binomial distribution:
$$\mathbb P (\mbox{"obtaining $x$ times 6 in $n=4$ random experiments"})=\binom{n}{x}p^xq^{n-x},$$
where $p$ is the probability of obtaining '$6$' and $q$ is $(1-p)$.
PS: The probability of obtaining '6' at least one time is the sum of the probabilities of getting '6' one time, getting '6' two times,..., getting '6' four times.
