A shelf in the Metro Department Store contains 80 colored in

A shelf in the Metro Department Store contains 80 colored ink cartridges for a popular ink-jet printer. Seven of the cartridges are defective.

If a customer selects 2 cartridges at random from the shelf, what is the probability that at least 1 is defective? (Round your answer to three decimal places.)

Solution

Note that

P(at least one defective) = 1 - P(0 defective)

Note that the probability of x successes out of n trials is          
          
P(x) = C(N-K, n-x) C(K, x) / C(N, n)          
          
where          
N = population size =    80      
K = number of successes in the population =    7      
n = sample size =    2      
x = number of successes in the sample =    0      
          
Thus,          
          
P(   0   ) =    0.83164557

Thus,

P(at least 1 defective) = 1 - 0.83164557 = 0.168 [ANSWER]