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Topic: coin toss
Replies: 9   Last Post: Sep 7, 2005 11:58 PM

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BlankMondragon

Posts: 4
Registered: 6/4/05
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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