If I had a container filled with 10 coke 8 sprite and 7 rootbeer what are the odds of choosing 3 sprite?

Question

Choosing 3 sprite from the container all at the same time.

Answer 1

very good if you are looking at the bottles in the container

Answer 2

First, we'll make some fairness assumptions.   Let's say that all the containers are the same size and shape as each other so the chance of blind grabbing one container is the same as the chances of blind grabbing one of the other containers instead.  And I'll assume too that you are blind grabbing, not being guided by reading the labels.   And that the containers are thoroughly randomized in the bucket.  And no one else is adding or subtracting containers from the bucket during the experiment.

I assert that reaching in with both hands and blind grabbing 3 containers at once is the same as reaching in 3 times and blind grabbing one container each time, so long as you don't put back (that is "reject") a container before you've gotten 3 containers.  

On the first grab, there are 10+8+7 containers (I'll just saw "cans") and 8 of them are sprite.

For the first can pulled out, the odds of it being a sprite are 8/25.   If the first can was a sprite, the odds of the 2nd can being a sprite are 7//24.   If can 1 & 2 were sprite, the odds of the 3rd can being a sprite are 6/23.   So the odds of hitting a sprite trifecta are (8/25)*(7/34)*(6/23), which by my calculator works out to just over .017, which means the chances of randomly accomplishing this feat are less than 1 chance in 50.   Not like the odds against hitting the mega-millions lottery,, but still not very likely an event to happen.

The good news, assuming you like sprite, is that the odds of not getting any sprite at all in your first 3 draws is only like 1 in 3.   That is, 2 out of 3 times of trying a 3-can experiment, at least one of the first 3 cans drawn is going to be a sprite.   I'll leave the arithmetic and details up to you..

Answer 3

I think it would be 8/25 x 7/24 x 6/23 x100= .32 x .291667 x .26087 x 100 =2.434783%