Question

Naval intelligence reports that 10 enemy vessels in a fleet of 17 are carrying nuclear weapons. If 6 vessels are randomly targeted and destroyed, what is the probability that less than 5 vessels transporting nuclear weapons were destroyed? Express your answer as a fraction or a decimal number rounded to four decimal places.

Answer 1

Number of ways to select r items from n, nCr = n!/(r! x (n-r)!)

P(less than 5 vessels transporting nuclear weapons were destroyed) = 1 - P(5 or more vessels carrying nuclear weapons were destroyed)

= 1 - (Number of ways to select 5 vessels carrying nuclear weapon from 10 x Number of ways to select 1 vessel not carrying nuclear weapon from 1 + Number of ways to select 6 vessels carrying nuclear weapon from 10)/Number of ways to select any 6 vessels from 17

= 1 - (10C5 x 7C1 + 10C6)/17C6

= 1 - (252 x 7 + 210)/12,376

= 0.8405