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Answer:
0.055 = 5.5% probability that exactly 5 employees were over 50.
Step-by-step explanation:
The employees are removed 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:
7 + 18 = 25 employees, which means that
7 over 50, which means that
10 dismissed, which means that
What is the probability that exactly 5 employees were over 50?
This is P(X = 5). So
0.055 = 5.5% probability that exactly 5 employees were over 50.