In a class of 16 students 4 are math majors A group of four

In a class of 16 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?

Solution

there are total 16 students

4 are with math major which means 16-4 = 12 students without math major.

a) probability of no student with math major = 12/16 = 3/4

b)atleast one math major = 1 - no math major

= 1-3/4 = 1/4

c)probability of havin 2 math major = 16C2*(1/2)^2*(3/4)^14 = 0.1336