Question

In a class of 18 students, 4 are math majors. A group of four students is chosen at random. (Round your answers to four decimal places.)

(a) What is the probability that the group has no math majors?

(b) What is the probability that the group has at least one math major?

(c) What is the probability that the group has exactly two math majors?

Answer 1

If p be the propbabilty of a student being Math major , then p= 4/18 = 0.2222

Let X be the rv counting the number of students in the group of 4 who are Math majors .

So, X~Bin( n=4, p=0.2222)

So,

x = 0,1,2,3,4

a) P[ Group has no math majors]

b) P[ Group has at leat one math major]

= 1- P[ No math major]

= 1- 0.3660

= 0.6340

c) P[ Group has exactly 2 math majors]