Question

Will Medal and Fan: Hard Probability Question (need thorough explanation):

A bag contains some marbles, each of which is one of four colors (red, white, blue, and green). There is at least one of each color. The composition of the bag is such that if we take four marbles out at random (without replacement), each of the following is equally likely:

(1) one marble of each color is chosen,

(2) one white, one blue, and two reds are chosen,

(3) one blue and three reds are chosen,

(4) four reds are chosen.

What is the smallest possible number of marbles in the bag?

Thanks.

Answer 1

one or two

Answer 2

supposed you have
r number of red
w number of white
b numb of blue and
g number of green

Answer 3

the prob you pick out
r w b g in that order is
r/(w+b+g) * w/((w+b+g)-1) * b/((w+b+g)-2) * g/((w+b+g)-3)
now this is only one case where we get it in that order,
ther are 4! ways where we still get r w b g in the end so the total prob of getting one of each color is

4!*(r/(w+b+g) * w/((w+b+g)-1) * b/((w+b+g)-2) * g/((w+b+g)-3) )

Answer 4

you can repeat this process, for all the 4 statments, and you will end up with 4 equations and 4 unknowns

Answer 5

The thing here is, that the solution you get will be the least number of each color needed, this will hold true if we scale all the balls up by the same factor, as the proportions will be the same,