Computing the Probability of Mutually Exclusive Events
Suppose the spinner in Figure 2 is spun again, but this time we are interested in the probability of spinning an orange or a . There are no sectors that are both orange and contain a , so these two events have no outcomes in common. Events are said to be mutually exclusive events when they have no outcomes in common. Because there is no overlap, there is nothing to subtract, so the general formula is
Notice that with mutually exclusive events, the intersection of and is the empty set. The probability of spinning an orange is and the probability of spinning a is . We can find the probability of spinning an orange or a simply by adding the two probabilities.
The probability of spinning an orange or a is .
A General Note: Probability of the Union of Mutually Exclusive Events
The probability of the union of two mutually exclusive events is given byHow To: Given a set of events, compute the probability of the union of mutually exclusive events.
- Determine the total number of outcomes for the first event.
- Find the probability of the first event.
- Determine the total number of outcomes for the second event.
- Find the probability of the second event.
- Add the probabilities.