Which is more likely to occur?

Question

Assume that 20% of the cars in Wheaton, Illinois are green. An observer stands at the intersection of Butterfield Road and Park Boulevard in Wheaton for an hour and sees 898 cars traveling along Butterfield and 243 cars traveling along Park. 
 a. In which direction is it more likely that more than 25% of the cars seen will be green?
     A) It is more likely among the 898 cars traveling on Butterfield Road.
     B) It is more likely among the 243 cars traveling on Park Boulevard.
     C) It is just as likely among either group of cars.

b. Suppose that you watch 20 cars in a row traveling along Butterfield Road at this intersection and not a single one is green. What is the probability that the next car will be green?

c. In answering parts a and b, what assumption have you made about the relationship between the colors of cars?

Please show answers and explain.

sheldonlinker · Accepted Answer

a)  The more cars you have, the more likely that 20% are green.  Thus, the street with less cars is more likely to be off the average by the given 5%.

b) The likelyhood of the next one being green is (20% of the total number of cars in the city - 898)/Total number of cars in the city.  That's real close to 20%.

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Which is more likely to occur?

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