Assume there are 21 homes in the Quail Creek area and 9 of them have a security
ID: 3396911 • Letter: A
Question
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.)
Assume there are 21 homes in the Quail Creek area and 9 of them have a security system. Six homes are selected at random:
Explanation / Answer
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]