Of the light bulbs made by Acme, 7% are defective. Only 2% of the light bulbs made by Baker are defective. An office buys over 1000 light bulbs per year. They order 75% of their bulbs from Acme and 25% from Baker. A light bulb is chosen at random and found to be defective. What is the probability that it was produced by Baker?
Accepted Solution
A:
Answer:The probability that the bulb was produced by Baker is: 2/23Step-by-step explanation:It is given that: Acme, produces 7% of defective light bulbs.and only 2% of the light bulbs made by Baker are defective.Also, 75% of the bulbs are ordered as made by Acme and 25% from Baker.Hence,The probability that the defective light bulb that is chosen at random is made by Baker is:Ratio of the defective light bulb made by baker to the total number of defective light bulbs.Hence, it is calculated as:[tex]Probability=\dfrac{0.25\times 0.02}{0.25\times 0.02+0.75\times 0.07}\\\\\\Probability=\dfrac{0.0050}{0.0575}\\\\\\Probability=\dfrac{50}{575}\\\\\\Probability=\dfrac{2}{23}[/tex]