Answer to Question #221083 in Economics for Ishaq

Question

A box contains 24 transistors, 4 of which are defective. If 4 are sold at random, find the
following probabilities.
a. Exactly 2 are defective. (5 marks)
c. All are defective. (5 marks)
b. None is defective. (5 marks)
d. At least 1 is defective. (5 marks)

Answer 1

a. Exactly 2 are defective:

$P(2) = C(2;4)×(1/6)^2×(5/6)^2 = 6×(1/6)^2×(5/6)^2 = 0.1157.$

c. All are defective:

$P(4) = (1/6)^4 = 0.00077.$

b. None is defective:

$P(0) = (5/6)^4 = 0.4823.$

d. At least 1 is defective:

P(>=1) = 1 - P(0) = 1 - 0.4823 = 0.5177.