You have 5 freshmen, 6 sophomores, 10 juniors, and 2 seniors in your probability class. The teacher

Question:

You have 5 freshmen, 6 sophomores, 10 juniors, and 2 seniors in your probability class. The teacher randomly selects 3 students to go to the board to do problems.
a. What is the probability all 3 students will be juniors?
b. What is the probability all 3 students will be from the same year?
c. What is the probability that at least one student will be a junior?
d. Given that at least one student will be a freshman, what is the probability that all 3 students will be freshmen?
e. What is the expected number of juniors selected each day?
f. What is the standard deviation of the number of juniors selected each day?
g. Assume that, every day, the teacher uses the same random method of selecting 3 students from the whole class. It is possible for the same student to be called on 2 days in a row but not twice in one class. What is the probability that the teacher will select only juniors for 2 days in a row? What is this?
Distribution
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