Answer:
1/5
Step-by-step explanation:
That little weird backwards E covers all the elements within the box in the diagram. There are x(x - 2) paintings from the 20th century, 2x + 8 British paintings, x paintings that are both British and come from the 29th century, and 10 that are neither of these. These should all add up to 60:
x(x - 2) + (2x + 8) + x + 10 = 60
x² - 2x + 3x + 18 = 60
x² + x - 42 = 0
(x + 7)(x - 6) = 0
x = -7 or x = 6
Obviously, we can’t have a negative number of paintings, so x = 6.
Out of the paintings, we choose one that is from the 20th century, and there are:
x + x(x - 2) = 6 + 6 * (6 - 2) = 6 + 24 = 30 paintings from the 20th century
x of these are also British, so since x = 6, the probability we’re looking for is:
6/30 = 1/5
The answer is 1/5.
