Some watches were manufactured with some minor defects on th

Some watches were manufactured with some minor defects on the glass. It was determined that out of 60 watches, there were 10 defective. If we sample with replacement 10 of those watches, what is the probability (in percentage form) that exactly 2 of them are (is) defective?

Solution

Note that the probability of x successes out of n trials is          
          
P(n, x) = nCx p^x (1 - p)^(n - x)          
          
where          
          
n = number of trials =    10      
p = the probability of a success = 10/60 =   0.166666667      
x = the number of successes =    2      
          
Thus, the probability is          
          
P (    2   ) =    0.290710049 = 29.071% [ANSWER]