Weekly Challenge #140
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Outputs
Inputs
No data needed for this challenge
This week we will run an anecdotal workflow to prove the Birthday Paradox! The Birthday paradox simply refers to the phenomenon that if you assembled 23 people into one room, the chances of two people having the same birthday are 50-50. We could 'math' this out, but why not just assembles and simulate 100s of thousands of people in the seconds to prove it?
In this challenge, your goal is to build a table that increment group sizes from 2 people all the way to 50 people. In each of those group sizes, run 1000 random trials and see what percent of groups had at least one set of people match. Why 1000? Theoretically, the more trials you run, the more likely you are to get a refined percent (e.g. flipping a coin four times may not a perfect 50-50 chance where it would be much closer after 1000 flips).
Due to the nature of this challenge, you will need to generate your own data! I have provided a sample output of mine, but since we are randomly assigning birthdays, you may find small differences in our answers. At what group size did it exceed 75% chance? 90% chance?
2
0.005
3
0.01
4
0.021
5
0.029
6
0.037
7
0.059
8
0.067
9
0.085
10
0.11
11
0.154
12
0.168
13
0.195
14
0.217
15
0.255
16
0.274
17
0.334
18
0.329
19
0.386
20
0.414
21
0.465
22
0.488
23
0.49
24
0.539
25
0.559
26
0.614
27
0.609
28
0.657
29
0.671
30
0.688
31
0.758
32
0.752
33
0.775
34
0.777
35
0.82
36
0.832
37
0.851
38
0.884
39
0.858
40
0.894
41
0.9
42
0.901
43
0.908
44
0.93
45
0.93
46
0.946
47
0.957
48
0.959
49
0.964
50
0.976
C:\ProgramData\Alteryx\Engine\Engine_4108_63735581a377433997497b67acb339e3_\Engine_21392_db96703b14c641619f3a76b68bdc6ab0_.yxdb
Single
Profile
GroupSize
Int32
4
2
[GroupSize] <= 50
[GroupSize] + 1
Iteration
Int32
4
1
Iteration<= 1000
Iteration+ 1
Allow
[Count] > 1
Simple
>
Count
True
fixed
2018-11-07 13:25:39
0
1
2018-11-07 13:25:39
2018-11-07 13:25:39
[Count] > 1
GroupSize
PersonCount
Int32
4
1
[PersonCount]<=[GroupSize]
[PersonCount]+ 1
scatter
markers
GroupSize
Probability
Chance same birthday
sans-serif
true
closest
false
700
849
-1.1899529042386181
53.189952904238616
true
linear
Group Size
-0.055061553985872869
1.0430615539858727
true
linear
Probability
C:\ProgramData\Alteryx\Engine\Engine_4108_63735581a377433997497b67acb339e3_\Engine_21392_8f4493a0739a4a598c643b0ffa6649ba_.yxdb
Single
Report
Horizontal
challenge_140_solution