Question

A manufacturer of ovens knows that 1 out of every 124 ovens will be manufactured with some sort oferror. If the manufacturer tests 43 of these ovens at random before they leave the factory, what is theprobability in terms of percent chance that none of these ovens are defective (round your answer to thenearest hundredth)?

Answer 1

This problem is an example of two probabilities happening at the same time. Out of 124 ovens, only 1 oven may have some sort of error. This means that the rest are good-quality ovens. Since the second event deals with testing 43 ovens that do not have any error, we look first at the probability of getting a good quality oven at over 124 ovens. There are 123 good quality ovens over 124 ovens, hence, the probability of getting a good quality oven is

`P=(123)/(124)`

The second event is to randomly test 43 samples, wherein all of these samples are not defective. But there is still a chance that one out of these 43 samples is defective. Hence, the probability for this event is

`P=(42)/(43)`

Multiplying the probabilities

`\begin{gathered} P=(123)/(124)\cdot(42)/(43)=0.96886 \\ P=0.96886*100\%=96.89\% \end{gathered}`

Hence, the probability in terms of percent for the event given is 96.89%.