Simple Question

#1
Here is a simple one but I am having a brain fart this morning.

Say you have a drawing, with replacement. The odds of winning are 1 in 2500 and you draw 104 times. What are your combined odds of winning?

My first thought is to take 1/2500 * 104 which then gives me 104/2500.

Let me know if this doesnt make sense.

Another way of putting it would be, say I have a drawing where there are 2500 names in the bowl and I will be drawing from it 104 times each time replacing the name. What are the odds that any one person would win at least once?
 
Last edited:

Mean Joe

TS Contributor
#2
1/2500 * 104 doesn't make sense; since drawing is done with replacement, then it's possible to do 10,000 drawings and not win.

This type of problem can be done by calculating the probability of losing every time; then subtract from 1, to get the probability of winning at least once.

P{not winning in 1 drawing} = 2499/2500
P{not winning in 104 drawings} = (2499/2500)^104
P{winning at least once in 104 drawings} = 1 - (2499/2500)^104