Question

Approximately 15% of the students in ST130
obtain A grade. If 3 students are selected at
random, find the probability that
a)all of them obtain A grade in ST130.
b)Exactly 2 obtain A grade in ST130.
c)at least one obtain A grade in ST130

Answer 1

prob of A = .15
prob of notA = .85

a) prob all 3 to get A = (.15)^3 = .003375

b) exactly 2 A's = C(3,2) .15^2 (.85)
= .057375

c) at least one
= 1 - prob no A's
= 1 - .85^3 = .385875

or the long way:
prob oneA + prob 2 A's + prob 3 A'a
= C(3,1) (.15)(.85)^2 + C(3,2) (15)^2 (.85) + C(3,3) (.15)^3
= .325125 + .057375 + .003375
= .385875