The probability of event A occurring is expressed as P(A). P(A) is the number of outcomes favorable to the event, divided by total number of outcomes. The probability of throwing a three with one die is one in six (there are six possible numbers, or outcomes, on a die), and is expressed as P(A) = 1/6 (as a fraction).
The probability of either event A or event B happening is expressed as P(A U B). To express the probability of either a 3 (event A) or a 5 (event B) occurring with the roll of a die, write P(A U B) = 2/6, reduced to 1/3. This probability is derived simply by adding the probabilities of event A and event B.
The probability of one event (event A) happening, given the occurrence of another event (event B) is called conditional probability, and is expressed as P(A/B). This is read as "the probability of A, given B." In the roll of the two die, P(A/B) is the same as P(A) or P(B), expressed as 1/6, because the events are independent of one another. The probability of a 5 coming upon the second die is always just 1 in 6, regardless of whether a 3 comes up on the first die.
The probability of both event A and event B happening is expressed as P(A**B). In this case, the asterisks should be written as an upside-down "U." To express the probability of both a 3 turning up on the first die rolled (event A) and a 5 turning up on the second die (event B), write P(A**B) = 1/36. The formula for deriving this probability is P(A+B) = P(A)P(B/A), which is the probability of event A occurring times the probability of event B occurring, given A. In the example of the die, P(B/A), remember from the section above, P(B/A) is the same as P(B).