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
[tex]P=\frac{123}{124}[/tex]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
[tex]P=\frac{42}{43}[/tex]Multiplying the probabilities
[tex]\begin{gathered} P=\frac{123}{124}\cdot\frac{42}{43}=0.96886 \\ P=0.96886\times100\%=96.89\% \end{gathered}[/tex]Hence, the probability in terms of percent for the event given is 96.89%.
