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Answer:
0.001687 = 0.1687% probability that no more than 1 vessel transporting nuclear weapons was destroyed.
Step-by-step explanation:
The vessels are destroyed and then not replaced, 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:
Fleet of 18 means that
9 are carrying nuclear weapons, which means that
9 are destroyed, which means that
What is the probability that no more than 1 vessel transporting nuclear weapons was destroyed?
This is:
In which
Then
0.001687 = 0.1687% probability that no more than 1 vessel transporting nuclear weapons was destroyed.