Probability in consecutive events with a range of acceptable outcomes

Question

There are 82 balls in a bag.

25 balls are red, 57 balls are blue (the balls are otherwise identical and equally likely to be drawn).

I draw 10 balls consecutively without replacement.

What is the probability that, of the 10 balls that I draw, at least 3 are red?

Answer 1

This is 1 - the probability that 2 or less are red.

This a hypergeometric distribution (drawing without replacement).

From Excel, we can use = 1-HYPGEOM.DIST(2,10,25,82,1) = 0.642955602834561

Note that 25/82 * 10 = 3 2/41 = 3.04878, so we should expect 3 or more to be greater than 1/2.