Final answer:
The probability of the restaurant buying at least three nondefective microwave ovens can be calculated using combinations to find the total number of favorable outcomes divided by the total number of possible selections of 4 ovens from 7.
Step-by-step explanation:
The student is asking about the probability of the restaurant buying at least three nondefective microwave ovens out of four when there are 2 defective units in a shipment of 7. To solve this problem, we need to use combinatorics to find all the possible ways of selecting 4 out of the 7 ovens and then determine the number of these ways that include at least three nondefective units.
There are two scenarios that satisfy at least three nondefective units: either 3 nondefective and 1 defective, or all 4 nondefective. We can calculate the probabilities for these two scenarios:
Probability of 3 nondefective and 1 defective unit:
The total number of ways to choose 3 nondefective units out of 5 is a combination calculation, C(5,3). The number of ways to choose 1 defective unit out of 2 is C(2,1). So, the total number of favorable outcomes for this scenario is C(5,3) * C(2,1).
Probability of 4 nondefective units:
Similarly, the total number of ways to choose 4 nondefective units out of 5 is C(5,4). There is only 1 way to not choose any defective units (since we're choosing all nondefective units), so the total number for this scenario is C(5,4) * 1.
To find the total number of possible selections of 4 ovens, we calculate C(7,4). The probability of at least 3 nondefective units is the sum of the probabilities of the two scenarios divided by the total number of possible selections:
(C(5,3) * C(2,1) + C(5,4)) / C(7,4)