In a class, there are 13 students. Out of those 13, 5 students are freshmen. If we pick three students, without replacement, what is the chance that at least one of them is a freshman?

Question

1.    In a class, there are 13 students. Out of those 13, 5 students are freshmen. 

a)    If we pick three students, without replacement, what is the chance that at least one of them is a freshman?

b)    If we pick two students, without replacement, what is the chance that one of them is a freshman and one of them is not a freshman?

c)    If we pick five students, with replacement, what is the chance that two of them are freshmen and three of them are not freshmen?

Answer 1

a) 8 = 13 - 5; 1 - P(0) = 1 - P(8,3)/P(13,3) = 1 - (8*7*6)/(13*12*11) = 1 - 28/143 = 115/143 = .8042

b) C(8,1)C(5,1)/C(13,2) = 8*5/(13*12/2) = 20/39 = .5128

c) Note that this is with replacement. C(5,3)(8/13)³(5/13)² = 10 * 512/2197 * 25/169 = 128000/371293 = .3447