A round carpet in the center of the room has a diameter of 32 cm the room is 300cm x 500 cm the probability of Dust landing in the room but not on the carpet is 99.5%

I don't know what the question is, but the area of the carpet divided by the area of the room is 256pi / (300x500) =.00536, which is 99.5% or 1-.00536 of not landing on the carpet

The probability of dust landing on the carpet is the area of the carpet divided by the area of the room, and the probability of landing in the room but not the carpet is 1-P (C)

P (R! C) = 1-P (C)

P (R! C) = 1 - (((π32^2) / 4) / (300*500))

P (R! C) = 1-16π/9375

P (R! C) = (9375-16π) / 9375

P (R! C) ≈0.994638

P (R! C) ≈99.5% (to nearest tenth of a percent)