Question

I ate five M&Ms: red, green, green, red and yellow. Only these three colors are possible. I assume that p(yellow)=3p(green)

What is the estimated probability of green color?

Answer 1

Below is code written in a free CAS (WxMaxima):

The above code creates the probability of 19 or more brown in the sample of 48 for population sizes from 5*19 to 10000 in steps of 5.

Here’s a plot of that data:

The horizontal blue line is the probability for an infinite population size (or, choosing each of the 48 M&Ms with replacement, which I infer is not what you meant). It is calculated using the binomial cdf:

The red curve approaches the blue line asymptotically as the population gets larger.

At population 10000, the red curve is

.