Question

somebody is looking for a top-floor apartment. she haers about two vacant apartments in a building with 7 floors en 8 apartments per floor. what is the probability that there is a vacant apartment on the top floor

Answer 1

The probability that there is a vacant apartment on the top floor will be 0.2675

The total number of apartments available in the whole building will be 7×8 = 56 as there are 8 apartments on every floor and in total there are 7 apartments.

Now the person wants to select 2 apartments from the building

so total permutations of selecting 2 apartments will be 56C2 = 1540

The number of ways of selecting one apartment vacant on the top floor will be

8C1× 48C1 = 384

The number of ways of selecting two apartments from the top floor will be 8C2 =28

total number of ways of selecting vacant apartment from the top floor will be 384+28 = 412

Therefore, the probability that there is a vacant apartment on the top floor will be 412/1540 = 0.2675