# Quick probability question

1. Jun 28, 2008

### hxtasy

Let's say you have 100 marbles in a jar, one of them is unique. The chances of that "one" being picked would be 1/100 or 1%.

Now let's say you picked a handful of marbles, 16 at a time, what would be the probability that that unique "one" would get picked again?

My guess is 100/16 = 6.25, and then 1/6.25 or 16%. Is this correct?

What would the technical term for this type of grouping probability be?

thanks!

2. Jun 28, 2008

### HallsofIvy

Staff Emeritus
Well, if you kept the unique one in your hand after picking it the first time, the probability is 0! So I am going to assume that the "unique" marble has been replaced. This is called "sampling with replacement".

Strange way to do that calculation. Why not just 16/100?

The probability that specific marble will be picked on any one trial is 1/100 and the probability that some other marble will be picked in 99/100. If you pick 16 marbles, the probability that specific marble will be a specific one (if you set all 16 in a row, the probability is will be, say, the 9th marble in the row) will be (1/100)(99/100)15= 9915/10016. But there are 16 different such positions so the probability the unique marble will be somewhere in that group of 16 is (16)(9915/10016= 0.1376 or about 13.76%.

3. Jun 28, 2008

### hxtasy

Hey HallsofIvy thank you for the reply. I have never done one thing with probabilities before. As i read more about them online most examples are pretty simple but some I don't understand. I guess I was thinking about it in a weird direction, either way I am going to have to look at that last paragraph you wrote it is slightly confusing.

thanks