What is the probability of finding the parking lot empty?

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The probability of finding the parking slot occupied is 1/3. You find it empty for 9 consecutive days. Find the probability that it will be empty on the 10th day.

Jul 08 '2014 at 10:20AM

1 Answer

This is a classic tricky probability question.

A tip for probability questions: never hurry while doing them and think the logical answer, even if it seems wrong at the first time, go for the logical ones. Sometimes we feel there might be a hidden trick, sometimes it is but many times it is NOT.

The answer to this question is 2/3, why ? Read the question carefully, it says what is the probability of finding it empty on the 10th day. Now in probability if an event has already happened it cannot have an effect on the probability of an event to occur in future. The parking slot has been empty for 9 days but that does not effect the 10th day.

Had the question been what is the probability of finding a parking slot empty for 10 consecutive days then the answer would have been (2/3)^10.

Jul 08 '2014 at 10:20AM

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