If a die is thrown $5$ times, what are the odds of getting a $5$ AT LEAST $3$ times

Question

The probability of getting a $5$ three times is $0.03215$ but as we are looking for a $5$ to be rolled at least $3$ times, does that mean we add up the probabilities for getting a $5$ four and five times as well?

Answer 1

If $X$ is the number of 5s, then $X\sim B\left(5,\frac{1}{6}\right)$. The probability of getting at least 3 fives is $$\mathbb P(X=3)+\mathbb P(X=4)+\mathbb P(X=5)$$ meaning that you have to sum the probabilities for getting 3, 4 and 5 fives.

Answer 2

Here is a graph representation of your problem

The result is the sum of the 3 yellow bars (the latest 2 are very low...but they exist)

Same solution if you calculate 1 minus the burgundy bars