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Re: coin toss
Posted:
Sep 7, 2005 11:58 PM
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Fakename wrote:
: If you toss 100 coins, what's the probability of getting 5,
: either heads or tails, in a row? 6 in a row?
: How do you figure it out?
You can make a simulation.
Create a list of 100 tosses:
[1 1 0 0 1 0 0 1 0 1 1 1 1 0 1 1 0 0 0 1 1 1 1 1 1 1 0 1 1 1 0 1 0 1 1
0 0 1 0 1 0 1 1 1 0 0 0 0 0 1 1 1 0 0 0 0 0 1 1 0 0 0 1 1 0 1 0 1 0 0 1
1 1 0 0 1 1 0 0 1 1 0 0 1 0 1 0 1 1 0 0 1 1 1 1 1 0 1 1 1]
group them:
[[1 1] [0 0] [1] [0 0] [1] [0] [1 1 1 1] [0] [1 1] [0 0 0] [1 1 1 1 1 1
1] [0] [1 1 1] [0] [1] [0] [1 1] [0 0] [1] [0] [1] [0] [1 1 1] [0 0 0 0
0] [1 1 1] [0 0 0 0 0] [1 1] [0 0 0] [1 1] [0] [1] [0] [1] [0 0] [1 1
1] [0 0] [1 1] [0 0] [1 1] [0 0] [1] [0] [1] [0] [1 1] [0 0] [1 1 1 1
1] [0] [1 1 1]]
count the members of each group:
[2 2 1 2 1 1 4 1 2 3 7 1 3 1 1 1 2 2 1 1 1 1 3 5 3 5 2 3 2 1 1 1 1 2 3
2 2 2 2 2 1 1 1 1 2 2 5 1 3]
find the maximum of those:
7
is that number greater than or equal to 5 (if 5 is what you want)
1
(1 means true, 0 means false)
Create a list of many such experiments (here I show 100 if them):
[1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1]
find the average
0.99
If you try with 1000 experiments instead of just a 100 you'll get
values like:
show simul 5
0.975
show simul 6
0.84
show simul 7
0.548
show simul 8
0.3
show simul 9
0.15
show simul 10
0.081
Daniel
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