Assume there are 21 homes in the Quail Creek area and 9 of t

Assume there are 21 homes in the Quail Creek area and 9 of them have a security system. Six homes are selected at random:

What is the probability all six of the selected homes have a security system? (Round your answer to 4 decimal places.)

What is the probability none of the six selected homes has a security system? (Round your answer to 4 decimal places.)

What is the probability at least one of the selected homes has a security system? (Round your answer to 4 decimal places.)

Solution

a)

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 =    21      
K = number of successes in the population =    9      
n = sample size =    6      
x = number of successes in the sample =    6      
          
Thus,          
          
P(   6   ) =    0.001547988 [ANSWER]

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b)

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 =    21      
K = number of successes in the population =    9      
n = sample size =    6      
x = number of successes in the sample =    0      
          
Thus,          
          
P(   0   ) =    0.017027864 [ANSWER]

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c)

P(at least one) = 1 - P(0) = 1 - 0.017027864

= 0.982972136 [ANSWER]