Answer:
1/3
Explanation:
You want to find x in a Venn diagram with regions labeled (x(x-5)), x, 2x, and 20, when the total is ε = 100. And you want to know the probability that a British stamp is from the 20th century.
Sum of the parts
The whole is the sum of the parts:
ε = x(x-5) +x +2x +20
100 = x² -2x +20 . . . . . . . . simplify
81 = x² -2x +1 . . . . . . . . . subtract 19 to make a complete square
81 = (x -1)²
9 = x -1 . . . . . . . positive square root
x = 10 . . . . . . . . add 1
Probability
Now we know ...
P(B) = (x +2x)/ε = 30/100 = 0.3
P(T&B) = x/ε = 10/100 = 0.1
The probability that a British stamp is from the 20th century is ...
P(T|B) = P(T&B)/P(B) = 0.1/0.3
P(T|B) = 1/3