# Probability exercise with apples

We have a tree with 100 apples. There are 10 red apples and the rest are green. Lisa is picking apples at random. When she pick the 3rd red apple she stop. What is the probability that Lisa has exactly 7 green apples (in addition to the 3 red apples she picked)?

• We are counting unordered. Pick two red is ${10 \choose 2}$ and seven green is ${90 \choose 7}$ ways, so the chance of that is $\frac{{10 \choose 2}{90\choose 7}}{{100 \choose 9}}\approx 0.1767$ Then the chance of a red (from what is left) is $\frac 8{91}$ Dec 6 '13 at 17:41