Question

Find the probability that in seven tosses of a fair dice, 3 appears at most two times.

Answer 1

at most two times means
none
once
twice

you need to calculate the probability of each of these events, then add them up

Answer 2

it is a little ambiguous, but i take it to mean, since you are tossing two dice, that "3 appears at most two times" means "the total is 3 at most two times"

Answer 3

use binomial thm here

prob of rolling a 3 is 1/6
prob of not rolling a 3 is 5/6

\[P(X=k) = \left(\begin{matrix}7 \\ k\end{matrix}\right) (\frac{1}{6})^k (\frac{5}{6})^{7-k}\]

Answer 4

you have to add probabilities for
X = 0, 1, 2