Two light bulbs get mixed up with seven good ones If you tak

Two light bulbs get mixed up with seven good ones. If you take two of the bulbs, what is the probability that both are bad?

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 =    9 BULBS      
K = number of successes in the population =    2 bad bulbs      
n = sample size =    2 bulbs taken      
x = number of successes in the sample =    2 bad bulbs      
          
Thus,          
          
P(   2   ) = C(7,0) C(2,2) / C(9,2) =   0.027777778 [ANSWER]