Answer:
1a. x = 0.08; y = 0.03; z = 0.17
1b. P(B) = 0.25
Explanation:
Given a Venn diagram with some numbers filled in, you want to find the missing numbers given that the probability of at least one is 0.92, and of exactly one is 0.70.
How to solve
The missing values are found by understanding the given information and what that means in relation to the diagram.
At least one
The total area enclosed by the circles is the probability of "at least one." The total probability represented by the entire diagram is 1, so that means ...
x = 1 - 0.92 = 0.08 . . . . . . . area not in any circle
It also means that ...
0.26 +0.05 +y +z +0.41 = 0.92 . . . . . . . area enclosed by circles
y + z = 0.20 . . . . . . . . . . . . . . . . . subtract 0.72
Exactly one
The probability of exactly one is the sum of areas inside exactly one circle:
0.26 +y +0.41 = 0.70
y = 0.03
Using this with the above equation in y and z, we find ...
z = 0.20 -y = 0.17
Bandicoots
The area inside circle B is ...
0.05 +y +z = 0.05 +0.20 = 0.25
The probability a contributor sponsors Bandicoots Unbanned is 0.25.