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?
Answer:
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
