The probability of H in 100 coin flips follows a binomial distribution.


If you are interested in the split:


Notice that 45:55, 46:54, 47:53, 48:52, 49:51 splits are all more probable than 50:50 split.
Collectively, the probability of 45:55 to 49:51 split is 65% probable versus 8% probable for 50:50 split.

 

I noticed there's a built-in function for combinations in recent versions of Python:


Here's some output of probabilities in %:

>>> from math import comb
>>> n = 100
>>> [print(k, 100*comb(n, k)/2**n) for k in range(n+1)]    
0 7.888609052210118e-29
1 7.888609052210118e-27
2 3.9048614808440084e-25
3 1.2755880837423761e-23
4 3.093301103075262e-22
5 5.939138117904503e-21
6 9.403635353348797e-20
7 1.2627738903068384e-18
8 1.4679746474816996e-17
9 1.5005963063146263e-16
10 1.36554263874631e-15
11 1.1172621589742536e-14
12 8.286361012392381e-14
13 5.609228993004073e-13
14 3.4857351599382456e-12
15 1.998488158364594e-11
16 1.0616968341311906e-10
17 5.246031415707059e-10
18 2.4190033750204775e-09
19 1.0439909302719956e-08
20 4.228163267601582e-08
21 1.6107288638482217e-07
22 5.783980920182251e-07
23 1.96152396423572e-06
24 6.293222718589601e-06
25 1.9131397064512387e-05
26 5.518672230147804e-05
27 0.00015125249815960647
28 0.0003943368702018312
29 0.0009790432639493738
30 0.002317069058013518
31 0.0052320914213208475
32 0.011281697127223078
33 0.023247133474277856
34 0.045810527728724015
35 0.08638556657416528
36 0.15597393964779843
37 0.26979276047186757
38 0.44728799762441196
39 0.711073226992655
40 1.0843866711637988
41 1.5869073236543396
42 2.2292269546572867
43 3.0068642644214565
44 3.895255978909614
45 4.8474296626430755
46 5.795839814029764
47 6.659049999098027
48 7.352701040670738
49 7.802866410507722
50 7.958923738717876
51 7.802866410507722
52 7.352701040670738
53 6.659049999098027
54 5.795839814029764
55 4.8474296626430755
56 3.895255978909614
57 3.0068642644214565
58 2.2292269546572867
59 1.5869073236543396
60 1.0843866711637988
61 0.711073226992655
62 0.44728799762441196
63 0.26979276047186757
64 0.15597393964779843
65 0.08638556657416528
66 0.045810527728724015
67 0.023247133474277856
68 0.011281697127223078
69 0.0052320914213208475
70 0.002317069058013518
71 0.0009790432639493738
72 0.0003943368702018312
73 0.00015125249815960647
74 5.518672230147804e-05
75 1.9131397064512387e-05
76 6.293222718589601e-06
77 1.96152396423572e-06
78 5.783980920182251e-07
79 1.6107288638482217e-07
80 4.228163267601582e-08
81 1.0439909302719956e-08
82 2.4190033750204775e-09
83 5.246031415707059e-10
84 1.0616968341311906e-10
85 1.998488158364594e-11
86 3.4857351599382456e-12
87 5.609228993004073e-13
88 8.286361012392381e-14
89 1.1172621589742536e-14
90 1.36554263874631e-15
91 1.5005963063146263e-16
92 1.4679746474816996e-17
93 1.2627738903068384e-18
94 9.403635353348797e-20
95 5.939138117904503e-21
96 3.093301103075262e-22
97 1.2755880837423761e-23
98 3.9048614808440084e-25
99 7.888609052210118e-27
100 7.888609052210118e-29

that seems to agree with the web site originally posted,
thank you

 

Surely the probability of heads or tails is 100%?

 

As the number of flips increases the probability shrinks around flips/2, as shown in the graph. At 100 flips the probability that # of tails is between 49 and 51 is about 23%. But at 100,000 the probability that # of tails is between 49K and 51K is very near to %100.

At the limit, as flips increase, the distribution becomes a delta function centered at the 50% point. Central limit theorem.

 

Surely the probability of heads or tails is 100%?

Yes. And what does that mean to you?

 

Yes. And what does that mean to you?

Scientific research indicates that there's a 0.0167% change that a coin lands on its side[1]. So if what you say is true there's a 100.0167% probability that a coin toss has an outcome!

[1] Murray and Teare, The probability of a tossed coin falling on its edge, Phys. Rev. E. 2547-2552 (1993)

 

Scientific research indicates that there's a 0.0167% change that a coin lands on its side[1].

Same math climate "scientists" use, lol. Seriously, the definition of "flip a coin" disallows the edge outcome. In practice, you'd just flip it again, and ignore the edge roll.

 

Yes. And what does that mean to you?

IM very happy that the probability of H or T is 100 %, as its a perfect fair coin , that is re assuring..
but a bit off topic,

 

Thank you to all those that have taken this as it is intended , a serious question and discussion. Those people have made it very informative.