13.4 Compound Probability

• Compound Event – An event composed of more than one event.

• Compound Probability can be found by analyzing the probability of each event within the compound event.

• There are 2 types of events, independent and dependent.

• If the result of one event does not affect another event then the event is said to be independent.

• If the result of one event has some impact on a second event, the events are said to be dependent.

• Events that cannot happen at the same time are said to be mutually exclusive events.

• For example you cannot roll a 2 and a 5 on a number cube at the same time, therefore the events are said to be mutually exclusive. If two events A and B are mutually exclusive, then the probability of both occurring is 0. The probability of A or B occurring is the sum of the probability of A occurring and the probability of B occurring.

• These events are mutually exclusive, they cannot occur at the same time.

• P(Basketball or Swim) = P(Basketball) + P(Swim)

• Some events have overlapping occurrences. For example if we were asked the probability of choosing a red card or an ace from a standard deck of cards, we would be asking the following.

• P(Red or Ace) = P(Red) + P(Ace)• However, we must realize that some of the aces are also red

cards and some of the red cards are aces, so these are overlapping occurrences and we must remove one multiple of the occurrence. In P(Red) we have added in the red aces, and in P(Ace) we have added in the red aces, thus the red aces have been added in two times we only want them in the probability once. So we must adjust our formula.

• P(Red or Ace) = P(Red) + P(Ace) – P(Red and Ace)

• Is there an overlapping occurrence here?