There is a bag of marbles, each red or blue

Question

There is a bag of marbles, each red or blue. You pull 1 marble from the bag, it is red. you pull another, it is also red. You continue to pull marbles and all the ones you pull turn out to be red. How can this go on before you will be 99% confident that the majority of the marbles are red?

Answer 1

The problem can be restated as:

" What is the 99% confidence interval for the proportion of blue marbles to be 49% or less."

Let p be the desired proportion and N be the # of marbles in the bag

the confidence constant is z=

the error margin is E = z*sqrt( p * (1-p)/ n)

E^2 = z^2 * (p * (1-p)/ n) <--- the error margin as a function of the proportion and N

N*E^2/z^2 = p(1-p)

p^2 - p - N*E^2/z^2 = 0

Quadratic formula says:

p = [ 1 +or- sqrt ( 1 + 4* N*E^2/z^2)/2 <--- the proportion as a function of N and error margin

N = p(1-p)*z^2/E^2 <--- the sample size as a function of the proportion and error margin