1. ## Apartment vacancy question

My friend is in this exact situation and we are having trouble figuring out the probability - please help!

She is looking for a top-floor apartment in a building with 48 units. There are 6 floors and 8 units per floor. 2 units are currently vacant. What is the probability there is a vacant apartment on the top floor?

We came up with 1/24 (1/6 probability of top floor times 2/8 probability of vacancies on that floor) but are not sure if this is right. Thanks for your help!

2. ## Re: Apartment vacancy question

P(At least one vacancy on top floor) = 1 - P(No vacancies on top floor) = 1 - P(First vacancy isn't on top floor AND second vacancy isn't on top floor) = 1 - P(first vacancy isn't on top floor)*P(second vacancy isn't on top floor | first vacancy isn't on top floor) = 1 - (40/48)*(39/47) = 0.3085106

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