A psychology class consists of 32 freshmen and 48 sophomores. If the professor selects names from the class list using random sampling, a. what is the probability that the first student selected will be a freshman?
b. and if a random sample of n 5 6 students is selected and the first five selected are sophomores, what is the probability that the sixth student selected will be a freshman?
c. Repeat question a (above) after 10 sophomore students join the class.

b. and if a random sample of n = 6 students is selected and the first five selected are sophomores, what is the probability that the sixth student selected will be a freshman?

A) 0.4

B) 0.4267

C) 0.356

Explanation:

A) There are;

32 freshmen and 48 sophomores.

Thus, total number of students = 32 + 48 = 80 students.

Thus;

P(first student selected will be a freshman) = 32/80 = 0.4

B) Since there are 6 students randomly selected with the first 5 being sophomore, then;

After 5 sophomore students selected, we have;

(80 - 5) = 75 students left

Also, we have 32 freshmen.

Probability of the 6th being a fresh man which is the next selection is;

P(6th being a freshman) = 32/75 = 0.4267

C) if 10 sophomore students join, then total number of students is now;

80 + 10 = 90 students.

Thus;

P(first student selected will be a freshman after 10 sophomore students join) = 32/90 = 0.356

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