There are six colors of plain M&M candies: red, orange, yellow, green, blue, and brown. Your friend claims that each color is evenly distributed throughout their bags. For this problem, assume your friend's claim is true. You open a sample bag of plain M&M's and find that there are a total of 61 M&M's, of which 11 are red. You plan to buy a bunch more bags and create a distribution of the proportion of red M&M's that you find in each bag.

mu = 1/6 and p-hat = 11/61
What is the probability of getting that a bag of 61 M&M's has at least 11 red M&M's?
The answer is supposed to be 0.3873245603 but I don't know how to solve for it.

What is the probability that a jumbo bag of 366 M&M's has at least as high a proportion of red M&M's as the first bag (11 red out of 61 total)?
And this one is supposed to be 0.2415619279. I need work for this one too.