In the world of probability, compound events are probabilities of two or more things happening at once. For example, what is the probability that you forgot to do your homework andthere will be a pop quiz in class?

There are 2 types of compound events:

An exclusive compound event in one in which the multiple events do not overlap. The method for determining the probability of this type of compound event is to add together the probabilities of each event. The sum is the probability of the compound event. In mathematical terms:

P(C) = P(A) + P(B)

For example:

What is the probability of rolling either a two or a four using one 10-sided die?

The probability of rolling a two is 1/10 and the probability of rolling a four is also 1/10, and these 2 events are mutually exclusive. So, the compound probability is

P(C) = 1/10 + 1/10 = 2/10 or 1/5

Another example:

What is the probability of pulling any face card or a three of clubs from a standard deck of cards?

The probability of getting a face card is 12/52 and the probability of getting a three of clubs is 1/52, so the compound probability is

P(C) = 12/52 + 1/52 = 13/52 or 1/4

An inclusive compound event is one in which there is overlap between the multiple events. Problems like rolling a two or an even number are inclusive because two is an even number. The probability of pulling a club or a face card from a deck of cards is also inclusive because three of the face cards will be clubs.

The formula for determining the probability of an inclusive compound event is

P(C) = P(A) + P(B) - P(A and B)

For example:

What is the probability of rolling either a two or an even number using one 10-sided die?

The probability of rolling a two is 1/10 and the probability of rolling an even number is 5/10. However, the probability of rolling an even number that is 2 is 1/10, therefore, the compound probability is

P(C) = 1/10 + 5/10 – 1/10 = 5/10 or 50%