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.

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Presentation transcript:

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: Rules

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

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

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 How many total balls are available Chances of getting a ball of the kind desired

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 How many total balls are available Chances of getting a ball of the kind desired Table when Lotto machine picks “bad” ball last The chance of this happening is:

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 How many total balls are available 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!

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 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

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: or 1 in 81.07

Any Questions?