SOLUTION: A fast food restaurant has heard that some of its customers have been dissatisfied with the food and service. The restaurant wishes to check on this by sampling customers as they

Question 955222: A fast food restaurant has heard that some of its customers have been dissatisfied with the food and service.
The restaurant wishes to check on this by sampling customers as they exit. It decides to randomly survey 3
out of the first 10 customers one day. The restaurant will deem that the situation is acceptable if none of the
3 customers surveyed are dissatisfied. Now suppose that in reality, 2 out of the 10 customers (20%) are
dissatisfied.
a) What is the probability that the restaurant will happen to survey both dissatisfied customers?
b) What is the probability that the restaurant will conclude that the situation is acceptable?
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
A fast food restaurant has heard that some of its customers have been dissatisfied with the food and service.
The restaurant wishes to check on this by sampling customers as they exit. It decides to randomly survey 3 out of the first 10 customers one day.
The restaurant will deem that the situation is acceptable if none of the
3 customers surveyed are dissatisfied.
-----------------------
Now suppose that in reality, 2 out of the 10 customers (20%) are
dissatisfied.
a) What is the probability that the restaurant will happen to survey both dissatisfied customers?
# of dissatified pairs:: 3C2 = 3
# of random pairs 10C2 = 45
P(2 dis) = 3C2/10C2 = 1/15
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b) What is the probability that the restaurant will conclude that the situation is acceptable?
# of satisfied triples:: 8C3 = 56
total # of triples:: 10C3 = 120
Ans: 56/120 = 7/15
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Cheers,
Stan H.
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