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Fan Appreciation Night, Part 2

Resources for this lesson:

Key Terms:

Intersection
Union
Addition Rule

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Create and Analyze

The the probability of A or B is known as finding the probability of the intersection of A and B, and may also be written as the probability of A intersect B.  Let’s explore what finding the probability of A or B means for mutually inclusive events.  Since mutually inclusive events can occur at the same time, the situation can be represented with a Venn diagram:

This graphic shows two overlapping circles.  The non-overlapping part of the circle on the left is labeled A.  The non-overlapping part of the circle on the right is labeled B.  The overlapping region is labeled A and B.

To find the probability of the intersection of A or B, the probability of A or B , we cannot simply find the the probability of A occurring plus the probability of B, because the two probabilities overlap with the section the probability of A and B.  This section would be counted twice.

This graphic shows the two overlapping circles being separated.  On the left is an image of the probability of A.  The circle shows region A and the overlapping region A and B.  On the right is an image of the probability of B.  The circle shows region B and the overlapping region A and B

Since the the probability of A and B, the union of A and B, is counted twice, you would need to subtract one of these sections to find the the probability of A or B .  So, when events are mutually inclusive, you apply the Addition Rule,

the probability of A or B equals the probability of A plus the probability of B minus the probability of A and B.

Let’s explore how to find the probability of winning a t-shirt or a hat.

 

 

 

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