Naval intelligence reports that 4 enemy vessels in a fleet of 17 are carrying nuclear weapons. If 9 vessels are randomly targeted and destroyed, what is the probability that more than 1 vessel transporting nuclear weapons was destroyed

0.7588 = 75.88% probability that more than 1 vessel transporting nuclear weapons was destroyed

Step-by-step explanation:

The vessels are destroyed 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:

Fleet of 17 means that

4 are carrying nucleas weapons, which means that

9 are destroyed, which means that

What is the probability that more than 1 vessel transporting nuclear weapons was destroyed?

This is:

In which

So

Then

0.7588 = 75.88% probability that more than 1 vessel transporting nuclear weapons was destroyed

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step-by-step explanation: