Among the 300 employees of a company, 240 are union members, while the others are not. If the 8 of the employees are chosen by lot to serve on the committee which administers the pension fund, find the probability that
(a) 5 of them union members
(b) all of them union members
(c) at least 6 of them union members
(d) 2 to 4 of them union members
Answers
Given : Among the 300 employees of a company, 240 are union members, while the others are not
8 of the employees are chosen by lot to serve on the committee
To Find : probability that
(a) 5 of them union members
(b) all of them union members
(c) at least 6 of them union members
(d) 2 to 4 of them union members
Solution:
Total Employee = 300
Union members = 240 p = 240/300 = 4/5
Not union members q = 1 - 4/5 = 1/5
8 of the employees are chosen
n = 8
P(x) = ⁿCₓpˣqⁿ⁻ˣ
5 of them union members
x = 5
=> P(5) = ⁸C₅(4/5)⁵(1/5)³ = 0.1468
all of them union members
x = 8
=> P(8) = ⁸C₈(4/5)⁸(1/5)⁰ = 0.16777
at least 6 of them union members
= P(6) + P(7) + P(8)
= ⁸C₆(4/5)⁶(1/5)² + ⁸C₇(4/5)⁷(1/5)¹ + ⁸C₈(4/5)⁸(1/5)⁰
= 0.2936 + 0.33554 + 0.16777
= 0.7969
2 to 4 of them union members
= P(2) + P(3) + P (4)
= ⁸C₂(4/5)²(1/5)⁶ + ⁸C₃(4/5)³(1/5)⁵ + ⁸C₄(4/5)⁴(1/5)⁴
= 0.001147 + 0.009175 + 0.045875
= 0.0562
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