Five fair dice are rolled. What is the probability of at most two of the dice coming up a one or a six?
I have come up with an answer of $0.79$ using binomial distribution: I summed the probability of $0$, $1$ and $2$ successes, with a success being $1$ or $6$ rolled. I am uncertain if I have the correct answer or used the right approach. Is my answer correct?
Indeed, if $A$ is the event in which at most two dice equal 1 or 6:
$$P[A] = {{5}\choose{0}}\bigg(\frac{1}{3}\bigg)^0 \bigg(\frac{2}{3}\bigg)^5 + {{5}\choose{1}} \bigg(\frac{1}{3}\bigg)^1 \bigg(\frac{2}{3}\bigg)^4 + {{5}\choose{2}} \bigg(\frac{1}{3}\bigg)^2 \bigg(\frac{2}{3}\bigg)^3 = \frac{2^5 + 5 \cdot 2^4 + 10 \cdot 2^3}{3^5} = \frac{192}{243} \approx 0.79 $$