Statistics Probability Question

Question

A jar of candy contains 45 red jellybeans, 30 green jellybeans, and 60 purple jellybeans. Find the following probabilities.

Q: Now suppose 6 jellybeans are selected without replacement instead. What is the probability that exactly 4 of the jellybeans are red?

Answer 1

Patrick, you missed that it said without replacement. There are 45 red jellybeans of 135, and we want the probability of selecting 4 reds.

We can either use combinatorics, C(45,4)C(90,2)/C(135,6) = (Excel writes C as combin) 0.079437931029711

or use the hypergeometric distribution, HYPGEOM.DIST(4,6,45,135,0) (the final 0 says exact, not cumulative)

Answer 2

Find the probabilities of selecting a specific color for jellybeans.

P(Red) = 45/135 = 1/3

P(Green) = 30/135 = 2/9

P(Purple) = 60/135 = 4/9

Use the binomial coefficient for n choose k. This will represent 6 jellybeans to choose from and will select 4 of them being red.

[6! / (4!)*(2!)]*(1/3)⁴*(2/3)² = 15*(1/3)⁴*(2/3)² = 0.07985 ≈ 0.08

The probability of selecting exactly 4 red jellybeans is about 0.08.