Calculating Theoretical Probabilities!!? H E L P?

P(A U B) is the probability of rolling an even number and a prime number.

so

A U B = An occurrence of either an even number and/or (inclusive or) a prime number

with one dice it is either: 2, 4, 6, 1, 3, 5 (these are all possibilities)

n(A U B) is the number of times this event has happened

A couple of points:

1) by "rolling" are you referring to a six-sided die?

2) by "P(A U(upside down) B)" to you mean P(A∩B) - ie P(A intersection B)?

If so, with the sample set S = {1, 2, 3, 4, 5, 6}, with cardinality |S| = 6

A = {2, 4, 6}

B = {2, 3, 5}

So

A∩B = {2} and |A∩B| = 1

Hence P(A∩B) = |A∩B| / |S|

= 1/6

If by "rolling" you mean something else, then you need to state the sample space in order to determine the solution.