SOLUTION: A shipment of 120 burglar alarms contains 5 that are defective. If 3 of the alarms are randomly selected and shipped to a customer, find the probability that the customer will g

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Question 1011187: A shipment of 120 burglar alarms contains 5 that are
defective. If 3 of the alarms are randomly selected and
shipped to a customer, find the probability that the
customer will get one bad unit by using
(i) The formula for the hyper geometric distribution
(ii) The formula for the binomial distribution as an
approximate
Answer by mathmate(429) About Me  (Show Source):
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Question:
A shipment of 120 burglar alarms contains 5 that are
defective. If 3 of the alarms are randomly selected and
shipped to a customer, find the probability that the
customer will get one bad unit by using
(i) The formula for the hyper geometric distribution
(ii) The formula for the binomial distribution as an
approximate

Solution:
(i) using hypergeometric distribution
P%28x%29=C%28A%2Cx%29%2AC%28B%2Cn-x%29%2FC%28A%2BB%2Cn%29
where
x=number of success (defective units)=1
n=size of sample=3
A=number of defective units in batch=5
B=number of non-defective units in batch=120-5=115
C(n,r)=probability of choosing r objects out of n.
P%28X=1%29=C%285%2C1%29%2AC%28115%2C2%29%2FC%28120%2C3%29
=5%2A6555%2F280840=6555%2F56168=0.1167 approximately
(ii) using binomial distribution to approximate probability
Here, we assume that the probability of drawing a defective part remains constant at 5/120 over the three draws.
then
p=5/120=1/24
n=3 (sample size)
x=1 (# of defects)
P%28X=1%29=C%28n%2Cx%29%2Ap%5E%28x%29%2A%281-p%29%5E%28n-x%29
=C%283%2C1%29%2A%281%2F24%29%5E%281%29%2A%2823%2F24%29%5E%282%29
=529%2F4608=0.1148 approximately