2. Write down your choice of 5 different numbers between 1 and 36 Three ways to win. –In any order match: All 5 4 out of 5 3 out of 5 –Prize: Giant Book of Puzzles Based on Hoosier Lottery’s Lucky 5 game Website: http://www.in.gov/hoosierlottery/http://www.in.gov/hoosierlottery/ Rules

3. What are your chances of winning a prize? Goal: We will use probability rules to compute your chances of winning

4. 123456 78910101 1212 1313 1414 1515 1616 1717 1818 1919 2020 21212 2323 2424 2525 2626 2727 2828 2929 3030 3131 32323 3434 3535 3636 You pick numbers: 1, 3, 14, 21, 35 Now think of “good” - green and “bad” - red balls There are 5 “good” balls and 31 “bad” balls Conclusion: The chances of winning depend on the “good” balls being selected by the Lotto machine

5. Chance of matching 5 out of 5 Draw # 1 st 2 nd 3 rd 4 th 5 th The kind of ball you want How many balls of this kind are remaining 54321 How many total balls are available 3635343332 Chances of getting a ball of the kind desired

6. Chance of Matching 4 out of 5 Draw # 1 st 2 nd 3 rd 4 th 5 th The kind of ball you want How many balls of this kind are remaining 543231 How many total balls are available 3635343332 Chances of getting a ball of the kind desired Table when Lotto machine picks “bad” ball last The chance of this happening is:

7. Chance of Matching 4 out of 5 (Cont) Draw # 1 st 2 nd 3 rd 4 th 5 th The kind of ball you want How many balls of this kind are remaining 543312 How many total balls are available 3635343332 Chances of getting a ball of the kind desired Table when Lotto machine picks “bad” ball fourth The chance of this happening is: But, this is exactly the same as before!

8. Chance of Matching 4 out of 5 (Cont) SO… Probability(4 out of 5) = (# of ways 4 “good” and 1 “bad” ball can be picked) x 0.00008223 How many ways can we pick 4 “good” balls and 1 “bad” ball? –Answer: 5 (See Table) Different ways to pick 4 good and 1 bad ball Draw number 1 st 2 nd 3 rd 4 th 5 th 1 2 3 4 5

9. Chance of Matching 3 out of 5 How do you think you would calculate the chances of getting 3 out of 5 correct? Try it! 1.Calculate chance of getting 3 “good” balls in the first three draws and 2 “bad” balls in the last two draws. 2.Find the number of ways 3 “good” and 2 “bad” balls can be picked. 3.Multiply your answers from 1 and 2. 4.Check your answer: 0.01233440 or 1 in 81.07

10. Any Questions?