Re: [LogoForum] Re: coin tosses

The message below is being cross-posted from LogoForum.

Here's one way to calculate the probability: 
http://mathworld.wolfram.com/Fibonaccin-StepNumber.html
 
That shows how to calculate the probability for no consecutive runs of N tails using Fibonacci numbers, so you'd have to subtract that from 1 to get the probability of N consecutive tails showing up.  If my calculations are correct, the probability for N=5 is 81%, for N=6 it's 54.6%.  The probability for N consecutive heads or tails would be:
 
P(tailsrun) + P(headsrun) - P(tailsrun AND headsrun)
 
For N=5, I believe the probability of having both a tailsrun and a headsrun is P(tailsrun)*P(headsrun)=65.6% (right?), which means the probability of having a run of 5 in 100 tosses is:
 
81% + 81% - 65.6% = 96.4%
 
The probability of having a run of 6 in 100 tosses is:
 
54.6% + 54.6% - 29.8% = 79.4%
 
Brian
 


Daniel Ajoy <dajoy@xxxxxxxxxxxxxxxxxxxxx> wrote:

On 15 Sep 2005 at 8:43, LogoForum@xxxxxxxxxxxxxxx wrote:

> The original Daniel's question was: How to
> know how many heads and how many tails there would be in a 100 throws
> toss?

I already answered that question but the original question was
different and it was posted to a different mailing list.

The question was:

Here I'll 10 coins in sequence:

Head
Tail
Head
Tail
Tail
Tail
Tail
Tail
Tail
Head

There are 6 tails in a run. if I toss 100 fair coins in sequence
what is the probability of getting runs of 5 or more? What is the
probability of getting runs of 6 or more?

Daniel



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