A bubble gum machine has B black bubble gums and O orange bu

A bubble gum machine has B black bubble gums and O orange bubble gums (it\'s Halloween). If 5 cents get you r bubble gums, what is the probability that you will get k orange bubble gums in one purchase?

Solution

No of black bubble gums = B

No of orange bubble gums = O

For r bubble gums we have to pay 5 cents.

Out of r, k should be orange

Hence r-k should be black and k should be orange.

We assume without replacement and r bubble gums taken at a time

Prob (for k orange bubble) = \\frac{OCk(BC_{r-k})}{(0+B)Cr}