What Is the Probability of Picking the Unique Marble in a Handful?

[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!

 

[HallsofIvy]

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?

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".

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

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

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


thanks!

The probability that specific marble will be picked on anyone 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%.

 

[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