# Probability question

#### Cemre

Let's say we have 10 boxes and I open each of them one by one...

I open the 1st box, there is a toy car in it.
I open the 2nd box, there is also a toy car in it.
I open the 3rd box, there is also a toy car in it.
...
I open the 9th box, there is also a toy car in it. :) wow, I got 9 toy cars in 9 boxes...

what is the probability that 10th box also has a toy car in it?

also generalize 10 to any number...
what is the probability that nth box also has a toy car in it, if all n-1 boxes each have a toy car in them.

#### CRGreathouse

Science Advisor
Homework Helper
There are lots of ways to do this binomial confidence interval problem. One common way is prob = (# successes + 1) / (# trials + 2), which would suggest a 91% chance.

#### gmax137

what is the probability that 10th box also has a toy car in it?
Depends on where you're getting the boxes.

#### uart

Science Advisor
Yes this is a silly question, unless you give some more information there is no well defined answer.

About the best answer I could give (without any additional information) would be,

$$P = \frac{m-9}{n-9}$$

Where n is the number of "boxes" in the universe and m<n is number of boxes in the universe that contain toy cars. I know that's not a very useful answer, but you know that if you want a useful answer you have to ask a sensible question right.

#### HallsofIvy

Science Advisor
What CRGreathouse is suggesting is to use the sample data to estimate the probability that a single box contains a car. Of course, if you have gotten a car in every box so far, the "maximum likelihood" estimate of that probability is 1 but you can use the sample size to put bounds on a confidence interval for it.

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