Chance in Lottery Games
Topic
Chance in Lottery Games
Vocabulary
- Combination
- Permutation
- Probability
Student Exploration
What are your chances of winning the lottery?
- The California Fantasy 5 game is a state lottery game played across the state. Anyone eighteen-years-old or older can buy a ticket at a local convenience store. All you have to do is pick five lucky numbers from 1 to 39 on a Fantasy 5 slip. Then every day at 6:30pm entries are closed and the state draws the five Fantasy 5 numbers for the day. Read more about the pickings at http://www.calottery.com/play/draw-games/fantasy-5. Now for the winnings! You win if you get one of the four following outcomes. You pick 2 of the 5 winning numbers, you pick 3 of the 5 winning numbers, you pick 4 of the 5 winning numbers, and you pick 5 of the 5 winning numbers.
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- What is the probability of picking 5 of the 5 winning numbers?
Extension Investigation
- a. Why does this situation represent a Combination?
- b. How many different ways can all five of the Fantasy 5 numbers be picked?
- c. How many different ways can four of the five Fantasy 5 numbers be picked?
- d. If you were analyzing how many ways that two of the five numbers could be picked, how would you approach solving this problem differently?
- e. If you were asked to find the probability of picking four of the five Fantasy 5 numbers correctly, how would you approach that task?
- f. What would need to change in the problem in order for it to represent a Permutation?
Resources Cited
http://www.calottery.com/play/draw-games/fantasy-5
Connections to other CK-12 Subject Areas
- Permutations Problems
- Permutations and Combinations Compared
- Theoretical and Experimental Probability
