60 paintings. T= Painting from 20th century. B= British painting. A painting is chosen random.it is from the 20 century. Work out the probability it is British

Question

venn diagram shows:
10 is neither
x(x-2) is T
x = both T & B
2x+8 = B

Please help this is due in a few hourss!! I know that the answer is 1/5, but I do not understand it. Thank you.

Answer 1

Number(T or B) = Number(T) + Number(b) - number(T and B)
60 - 10 = x(x-2) + 2x + 8 - x
x^2 - 2x + 2x - x - 42 = 0
x^2 - x - 42 = 0
(x - 7)(x + 6) = 0
x = 7 or x = -6, but x must be a whole number, so
x = 7

so British ---- 2(7) + 8 = 22
Prob(british) = 22/60 = 11/30

Check:

filling in the Venn diagram:
intersection --- 7
T --- x(x-2) = 35, but 7 belong to boths, so T only = 28
B --- 2x +8 = 22, but 7 belong to both, so B only = 15
not in any ---- 10

7 + 28 + 15 + 10 = 60 , all accounted for

perhaps check the typing of your problem