<h3>
Answer: B) Mutually exclusive</h3>
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Work Shown:
P(A and B) = P(A) + P(B) - P(A or B)
P(A and B) = 1/5 + 7/20 - 11/20
P(A and B) = 4/20 + 7/20 - 11/20
P(A and B) = (4+7-11)/20
P(A and B) = 0/20
P(A and B) = 0
Events A and B are <u>mutually exclusive</u> because the probability of both events happening simultaneously is 0. One event or the other must happen, but both can't happen at the same time.
Here's a visual way to think about it: draw a rectangle, and then split the rectangle into two smaller parts. The two smaller parts don't have to be equal in area, size, or shape. Label the two smaller parts A and B. If you throw a dart at the rectangle, you'll land somewhere in region A, or region B, but not both regions at the same time. This is a demonstration of what it means to be mutually exclusive. Regions A and B do not overlap in any way.
