3 Consider a group of students in which there are 23 freshma

3) Consider a group of students in which there are 23 freshman, 31 sophomores, 15 ju- niors, and 6 seniors. Assume that their ages range from 18 to 26.
a) What is the minimum number of randomly selected students required to guarantee that at least 3 students are of the same year classification?

b) What is the minimum number of randomly selected students required to guarantee that at least 2 students are the same age?
c) What is the minimum number of randomly selected students required to guarantee that at least 3 students are freshman?

d) Based on the information given for the entire group of students, what is the largest number of students having the same age that could be guaranteed?
e) Find the probability that when picking 2 students at random you will get 2 freshman. f) Find the probability that when picking 2 students at random you will get 1 freshman and 1 senior.

g) Find the probability that when picking 2 students at random you will not get any seniors.

Solution

a) If 9 are selected then atleast 3 will be there. (Because even if equally selected 8, 2 will be each group 1 extra will belong to atleast one group)

b) Min = 5 to be selected

c) 55 should be selected

d) 31 sophomores will have the same agae.

e) Pr (2 freshman) =

f) Pr 1 fresh and 1 senio =

g) P (no seniors) =