In a batch of 20 bottles of their product the Restin Chemica

In a batch of 20 bottles of their product the Restin Chemical Company knows that 8 were contaminated. Assume that these 8 bottles are spread randomly throughout the batch. Restin’s best customer was recently sent 6 bottles from this batch and claims that 4 of them were contaminated. Find the probability that this could happen

Solution

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 =    20      
K = number of successes in the population =    8      
n = sample size =    6      
x = number of successes in the sample =    4      
          
Thus,          
          
P(   4   ) =    0.119195046 [ANSWER]