# Thread: Longest run in 50 tosses

1. ## Longest run in 50 tosses

Hello....

How do I find the longest run in fifty tosses of a coin?
To add to this question, how do I compare two sequences of coin tosses to differentiate between real toss and the fake toss?

2. ## Re: Longest run in 50 tosses

Longest run of what? Is the coin fair? What exactly is a "fake toss"?

3. ## Re: Longest run in 50 tosses

the coin is fair. A fake toss is what I predict the sample space can be like.

4. ## Re: Longest run in 50 tosses

Longest run of Heads, I mean...

5. ## Re: Longest run in 50 tosses

Originally Posted by hsetima
Longest run of Heads, I mean...
The longest possible run of heads in 50 tosses of a fair coin is ..... 50 heads. (Unlikely, yes. But impossible, no.)

6. ## Re: Longest run in 50 tosses

It may be possible. But is there any way of calculating it - maybe by relative frequencies based on an experiment?
But I managed to find a formula - log of n in base 2. In my case it gave me the longest run to be 5.6 - it can be either be of heads or tails, but I cant explain how.....

7. ## Re: Longest run in 50 tosses

Originally Posted by hsetima
It may be possible. But is there any way of calculating it - maybe by relative frequencies based on an experiment?
$\displaystyle \text{(longest possible run of heads)}=\text{(total of times that you flip the coin)}$

The possibility that you will flip a heads every single time always exists. If you flip a coin one million times in a row, then the longest possible run of heads is one million (extreeemely unlikely, but possible nevertheless).

8. ## Re: Longest run in 50 tosses

Originally Posted by hsetima
It may be possible. But is there any way of calculating it - maybe by relative frequencies based on an experiment?
But I managed to find a formula - log of n in base 2. In my case it gave me the longest run to be 5.6 - it can be either be of heads or tails, but I cant explain how.....
The longest possible run is 50 heads. The probability of it occuring is (1/2)^50.

But I think what you want and what you asked are two different things. Perhaps you want the longest expected run ....

9. ## Re: Longest run in 50 tosses

Yes Mr. Fantastic,
I want the longest expected run

10. ## Re: Longest run in 50 tosses

Originally Posted by hsetima
Hello....

How do I find the longest run in fifty tosses of a coin?
To add to this question, how do I compare two sequences of coin tosses to differentiate between real toss and the fake toss?
Post the real problem please.

If this is a homework problem or from a book post it exactly as worded.

If this is a practical problem post the context and what you are trying to do.

CB