Forming a function of heads vs. tails.

• Feb 25th 2008, 11:12 AM
Jim Newt
Forming a function of heads vs. tails.
Heres the procedure:

1. I take a 100 nickels into a bowl and shake.
2. Dump them all out on a table and remove all the "heads".
3. Put remaining nickels back into bowl and repeat until no nickels are left.

How do I write a functional form for the number of nickels remaining as a function of the number of shakes?

Thanks,

Jim
• Feb 25th 2008, 12:21 PM
colby2152
Quote:

Originally Posted by Jim Newt
Heres the procedure:

1. I take a 100 nickels into a bowl and shake.
2. Dump them all out on a table and remove all the "heads".
3. Put remaining nickels back into bowl and repeat until no nickels are left.

How do I write a functional form for the number of nickels remaining as a function of the number of shakes?

Thanks,

Jim

Being a completely random experiment, you should expect to lose half of the nickels after each shake...

$f(t)=100\left(\frac{1}{2}\right)^t$, where t is a non-negative integer