SOLUTION: round carpet in the center of a room has a diameter of 32 cm. The room is 300 cm � 500 cm. The probability of dust landing in the room, but not on the carpet, is 99.5% i would say

Question 472908: round carpet in the center of a room has a diameter of 32 cm. The room is 300 cm � 500 cm. The probability of dust landing in the room, but not on the carpet, is 99.5% i would say this statement is true do you agree?
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
assuming the probability of dust landing anywhere in the room is the same, then the probability should be in proportion to the area of the carpet versus the area of the room except where the carpet is laying.
the room is 300 cm * 500 cm = 150000 square cm.
the carpet is 32 cm in diameter.
this means it has a radius of 16 cm.
this means the area of the carpet is equal to pi * 16^2 = 804.2477193 square cm.
subtract 804.2477193 from 150000 to get 149195.7523 square cm.
149195.7523 / 15000 = .994638349.
round that off to the nearest 10th of a percent, and you get 99.5%.
the probability that the dust will land on the carpet is 849.23477193 / 150000 which equals .005361651.
round that off to the nearest tenth of a percent and you get .5%
99.5% and .5% equals 100%
the statement appears to be true to me also.
i agree.

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