Question

Naval intelligence reports that 5 enemy vessels in a fleet of 17 are carrying nuclear weapons. If 7 vessels are randomly targeted and destroyed, what is the probability that no more than 1 vessel transporting nuclear weapons was destroyed? Express your answer as a fraction or a decimal number rounded to four decimal places.

Answer 1

The number of ways of choosing 7 vessels from a fleet of 17 vessels is .

The number of ways of choosing vessels transporting nuclear weapons from a fleet of 5 are carrying nuclear weapons and from 17-5=12 vessels not transporting nuclear weapons is .

The probability of destroying vessels transporting nuclear weapons if 7 vessels are randomly targeted and destroyed is

This is called Hypergeometric distribution.

The number of ways of choosing 0 vessels transporting nuclear weapons from a fleet of 5 are carrying nuclear weapons and 1 from 17-5=12 vessels not transporting nuclear weapons is .

The number of ways of choosing 1 vessel transporting nuclear weapons from a fleet of 5 are carrying nuclear weapons and 0 from 17-5=12 vessels not transporting nuclear weapons is .

The required probability is