#2**+2 **

10 paintings fall outside the circles....so....50 fall inside...and we have

x(x - 2) + x + 2x + 8 = 50

x^2 -2x + 3x = 42

x^2 + x - 42 = 0 factor

(x + 7) ( x - 6) = 0

Setting both factors to 0 and solving for x gives x = -7 (reject) or x = 6

So...the total number of painitngs from the 20th century is x * (x - 2) = 6* (6 - 2) = 24 (1)

And of these, x = 6 were British (2)

So....the probability that a painting is British given that it is from the 20th cenury is (2) / (1) =

6 / 24 = 1 / 4 = 25%

CPhill
Apr 21, 2018