1. Use the Counting Rules to compute Probabilities

2. 2 of these and 4 of those A classic type of problem You have various subgroups. When you pick 6, what is the probability that you get 2 of this group and 4 of that group? Jellybeans: 30 red, 30 yellow, 40 other Choose 6. Find P(2 red and 4 yellow)

3. 2 red out of 30; 4 yellow out of 40 Analysis – you must THINK! – “This is a Fundamental Counting Principle situation… – One event is drawing 2 red out of 30 – The other is drawing 4 yellow out of 40 – FUNDAMENTAL COUNTING PRINCIPLE says to multiply how many ways for each of them. – Each of these events is modeled by a COMBINATION, because the order doesn’t matter. So how do you write it in Combination language?

4. Computing the Probability

5. Draw 5 cards, what is the probability of exactly 0 aces? We can do this with our earlier techniques: – P(first card not at ace) = ____ / 52, times … – P(second card not an ace) = ____ / 51, times … – P(third card not an ace) = ____ / 50, times … – P(fourth card not an ace) = ____ / 49, times … – P(fifth card not an ace) = ____ / 48

9. Probability of a Full House

10. Probability of a Flush

11. Powerball Jackpot

12. Powerball $200,000

13. Powerball $10,000

14. Powerball $7

15. Two ways to lose Match absolutely nothing at all – 5 out of the 54 losing white numbers – 1 out of the 38 losing red powerball numbers Or match 1 white number only – 1 out of the 5 winning white numbers – 4 out of the 54 losing white numbers – 1 out of the 38 losing red powerball numbers