Computing the Probability of the Union of Two Events
We are often interested in finding the probability that one of multiple events occurs. Suppose we are playing a card game, and we will win if the next card drawn is either a heart or a king. We would be interested in finding the probability of the next card being a heart or a king. The union of two events , is the event that occurs if either or both events occur.
Suppose the spinner in Figure 2 is spun. We want to find the probability of spinning orange or spinning a .
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The probability of spinning orange or a is .
A General Note: Probability of the Union of Two Events
The probability of the union of two events and (written ) equals the sum of the probability of and the probability of minus the probability of and occurring together which is called the intersection of and and is written as ).Example 3: Computing the Probability of the Union of Two Events
A card is drawn from a standard deck. Find the probability of drawing a heart or a 7.Solution
A standard deck contains an equal number of hearts, diamonds, clubs, and spades. So the probability of drawing a heart is . There are four 7s in a standard deck, and there are a total of 52 cards. So the probability of drawing a 7 is . The only card in the deck that is both a heart and a 7 is the 7 of hearts, so the probability of drawing both a heart and a 7 is . Substitute into the formula.
The probability of drawing a heart or a 7 is .