Question

A lightbulb company has factories in two cities. The factory in city A produces two-thirds of the company’s lightbulbs. The remainder are produced in city B, and of these, 1% are defective. Among all bulbs manufactured by the company, what proportion are not defective and made in city B?

Answer 1

Answer:

The proportion that is not defective and made in city B is 0.33

Step-by-step explanation:

Let A be the event "The light bulb does not defect" and B the event "The light bulb is produced in city B".

From the information given:

• The probability of B is $P(B)=\frac{1}{3}$
• The probability of not B is $P(B^c)=\frac{2}{3}$
• The conditional probability of A given B is $P(A|B)=0.99$
• The conditional probability of not A given B is $P(A^c|B)=1-P(A|B)=0.01$

We want to find the probability of both A and B $P(A\cap B)$

The conditional probability of events A given B is related by the formula

$P(A|B)=\frac{P(A\cap B)}{P(B)}$

Therefore

$P(A \cap B)=P(B)P(A|B)=\frac{0.99}{3}=0.33$