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Answer:
0.0430 = 4.30% probability that exactly 2 of the 4 receiving-sets selected by the engineer are defective.
Step-by-step explanation:
Sets are chosen from the sample without replacement, which means that the hypergeometric distribution is used to solve this question.
Hypergeometric distribution:
The probability of x successes is given by the following formula:
In which:
x is the number of successes.
N is the size of the population.
n is the size of the sample.
k is the total number of desired outcomes.
Combinations formula:
is the number of different combinations of x objects from a set of n elements, given by the following formula.
In this question:
Lots of 50 means that
5 are defective, which means that
4 are selected, which means that
Find the probability that exactly 2 of the 4 receiving-sets selected by the engineer are defective.
This is . So
0.0430 = 4.30% probability that exactly 2 of the 4 receiving-sets selected by the engineer are defective.