Question

The proportion of brown M&M’s in a milk chocolate packet is approximately 14% (Madison, 2013). Suppose a package of M&M’s typically contains 52 M&M’s. a.) State the random variable. b.) Argue that this is a binomial experiment Find the probability that c.) Six M&M’s are brown. Twenty-Five M&M’s are brown. e.) All of the M&M’s are brown. f.) Would it be unusual for a package to have only brown M&M’s? If this were to happen, what would you think is the reason?

Answer 1

(a) Random variable = x = number of brown M&M's in a milk cholate packet

(b) This is a Binomial Experiment because:
(i) n = Total number of trials = 52

p = Probability of success in a single trial = p = 0.14

(iii) The trials are independent

(c)

(i) n = 52

p = 0.14

q = 1 - p = 0.86

x = 6

(ii) For x = 25:

(iv) For x = 52

(f) It would be unusual for a package to have only brown M&M's because probability of such as event is lamost 0.

If there were to happen, the reason may be: (i) We have have come across a rare event, which will happen again after a large number of trials OR (ii) The claim that the proportion of brown M&M's in a milk chocolate packet iis approximately 14% is wrong.