Question

EasyElectrics supermarket orders light bulbs from suppliers, AA Electronics and AAA Electronics. EasyElectrics purchases 30% of its light bulbs from AA and 70% from AAA. Two percent of the light bulbs purchased from AA are defective, while three percent of the bulbs from AAA are defective. Find the probability that a randomly selected light bulb a) was purchased from AA and is defectivie b) is defective

Answer 1

Answer: (a) 0.006

(b) 0.027

Explanation:

Given : P(AA) = 0.3 and P(AAA) = 0.70

Let event that a bulb is defective be denoted by D and not defective be D';

Conditional probabilities given are :

P(D/AA) = 0.02 and P(D/AAA) = 0.03

Thus P(D'/AA) = 1 - 0.02 = 0.98

and P(D'/AAA) = 1 - 0.03 = 0.97

(a) P(bulb from AA and defective) = P ( AA and D)

= P(AA) x P(D/AA)

= 0.3 x 0.02 = 0.006

(b) P(Defective) = P(from AA and defective) + P( from AAA and defective)

= P(AA) x P(D/AA) + P(AAA) x P(D/AAA)

= 0.3(0.02) + 0.70(0.03)

= 0.027