Question

Five marbles are randomly selected with replacement. The probability that a black marble is chosen is 15%. Round to the nearest thousandth.
What is the probability that 2 marbles are black?
What is the probability that at least 2 marbles are black?

Answer 1

For the 1st part:
$$
{5\choose2}(0.15)^2(1-0.15)^3
$$
The second
$$
\sum_{n=2}^5 {5\choose n}(0.15)^n(1-0.15)^{5-n}\\
=1-\sum_{n=0}^1 {5\choose n}(0.15)^n(1-0.15)^{5-n}\\
$$
Does this make sense?