Probability using venn diagrams

Wait, so the total is 60, right? Okay \( x^2-2x-x+2x+8-x+x+10=60\)

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%