The symbol ∩ means intersection, .i.e. you need to find the numbers that belong to both sets A and C. Those numbers might belong to the set C or not, because that is not a restriction.
Then lets find the numbers that belong to both sets, A and C.
As you see, all the perfect fourths are perfect squares, so the intersection of A and C is completed included in A. this is:
A ∩ C = C or A ∩ C = 1, 16, 81
On the other hand, the perfect cubes are:
1^3 = 1 2^3 = 8 3^3 = 27 4^3 = 81
B = {1, 8, 27, 81}
That means that the numbers 1 and 81 belong to the three sets, A, B, and C.
In the drawing you must place the number 16 inside the region that represents the intersection of A and C only, and the numbers 1 and 81 inside the intersection of the three sets A, B and C.
We have the following given p1 - probability for outcome 1 p2 - probability for outcome 2 p3 - probability for outcome 3 v1 - amount of money that you will win or lose for outcome 1 v2 - amount of money that you will win or lose for outcome 2 v3 - amount of money that you will win or lose for outcome 3
Therefore, p1v1 + p2v2 + p3v3 is the average money you win or lose in playing the game.
