A store has 10 SpiderMan twin comforters for sale Two of the

A store has 10 Spider-Man twin comforters for sale. Two of the 10 have been stitched incorrectly at the factory and will split open when used. Suppose 4 of the comforters are randomly selected and let X be the number of comforters among those 4 that have been stitched incorrectly. State the distribution of X and the corresponding parameter(s). Find the probability that at least 1 of the 4 comforters have been stitched incorrectly.

Solution

1.

a)

This is a Hypergeomtric Distribution.

Note that the probability of x successes out of n trials is          
          
P(N, K; n, x) = C(N-K, n-x) C(K, x) / C(N, n)          
          
where          
N = population size = 10      
K = number of successes (stiched incorrectly) in the population =    2      
n = sample size =    4      
x = number of successes in the sample

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b)
  
P(at least 1) = 1 - P(0)

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 =    10      
K = number of successes in the population =    2      
n = sample size =    4      
x = number of successes in the sample =    0      
          
Thus,          
          
P(   0   ) =    0.333333333

Thus,

P(at least 1) = 1 - 0.33333333 = 0.6666667 [ANSWER]