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?

The probability that the bulb was produced by Baker is:

                                  2/23

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:

a negative exponent is translated as follows:

so, we have