Write down your choice of 5 different numbers between 1 and 36 Three ways to win. –In any order...
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Transcript of Write down your choice of 5 different numbers between 1 and 36 Three ways to win. –In any order...
• 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/
Rules
• What are your chances of winning a prize?
• Goal: We will use probability rules to compute your chances of winning
1 2 3 4 5 6
7 8 9 10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
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 # 1st 2nd 3rd 4th 5th
The kind of ball you want
How many balls of this kind are remaining 5 4 3 2 1
How many total balls are available 36 35 34 33 32
Chances of getting a ball of the kind desired
5
36
4
35
1
32
3
34
2
33
5 4 3 2 1Probability(5 out of 5) 0.00000265
36 35 34 33 32Another way to say this is: 1 in 376,992
Chance of Matching4 out of 5
Draw # 1st 2nd 3rd 4th 5th
The kind of ball you want
How many balls of this kind are remaining
5 4 3 2 31
How many total balls are available
36 35 34 33 32
Chances of getting a ball of the kind desired
Table when Lotto machine picks “bad” ball last
2
33
3
34
4
35
5
36
31
32
The chance of this happening is:
0.00008223 32
31
33
2
34
3
35
4
36
5
Chance of Matching4 out of 5 (Cont)
Draw # 1st 2nd 3rd 4th 5th
The kind of ball you want
How many balls of this kind are remaining
5 4 3 31 2
How many total balls are available
36 35 34 33 32
Chances of getting a ball of the kind desired
Table when Lotto machine picks “bad” ball fourth
31
33
3
34
4
35
5
36
2
32
The chance of this happening is:
5 4 3 31 2 0.00008223
36 35 34 33 32
But, this is exactly the same as before!
Chance of Matching4 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
1st 2nd 3rd 4th 5th
1
2
3
4
5
Probability(4 out of 5) 5 0.00008223 0.00041115
Another way to say this is: 1 in 2,432.21
Chance of Matching3 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
Any Questions?
