Question

A candy dish contains 100 jelly beans and 80 gumdrops. Fifty candies are picked at random. What is the probability that 35 of the 50 are gumdrops? The two groups are jelly beans and gumdrops. Since the probability question asks for the probability of picking gumdrops, the group of interest (first group) is gumdrops. The size of the group of interest (first group) is 80. The size of the second group is 100. The size of the sample is 50 (jelly beans or gumdrops). Let X = the number of gumdrops in the sample of 50. X takes on the values x = 0, 1, 2, ..., 50. What is the probability statement written mathematically?

Answer 1

The mathematical probability statement that needs to be calculated for the probability of picking 35 gumdrops out of 50 candies is P(X = 35), using the Hypergeometric Distribution.

Step-by-step explanation:

The student is dealing with a problem of calculating the probability of a certain outcome when sampling without replacement from a finite population. This falls within the realm of the Hypergeometric Distribution, which is useful for such situations where each pick is not independent. Since the question involves finding the probability of selecting a specific number of gumdrops out of a total sample. The appropriate mathematical statement to represent the probability that 35 of the 50 candies picked are gumdrops is given by:

P(X = 35) = [C(80, 35) * C(100, 15)] / C(180, 50)

where C(n, k) denotes the number of combinations of n things taken k at a time.