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A comprehensive introduction to mutually exclusive and not mutually exclusive events in probability, a fundamental concept in high school mathematics. It explains the definitions, formulas, and applications of these concepts through clear examples and step-by-step solutions to practice problems. Designed to help students understand the difference between these types of events and how to calculate probabilities involving them.
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2024/2025
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Events that cannot occur at the same time. MUTUALLY EXCLUSIVE EVENTS
Events that cannot occur at the same time. MUTUALLY EXCLUSIVE EVENTS If two events, A and B, are mutually exclusive, then the probability that either A or B occurs is the sum of their probabilities.
Events that occur at the same time. UNMUTUALLY EXCLUSIVE EVENTS
Events that occur at the same time. UNMUTUALLY EXCLUSIVE EVENTS If two events, A and B, are not mutually exclusive, then the probability that either A or B occurs is the sum of their probabilities decreased by the probability of both occuring.
A restaurant serves a bowl of candies to their customers. The bowl of candies Mario receives has 10 chocolate candies, 8 coffee candies, and 12 caramel candies. After Mario chooses a candy, he eats it. PROBLEM 1 Find the probability of getting candies with the indicates flavors. a. P (chocolate or caramel) b. P (coffee or not caramel)
Problem # 1 a. P (chocolate or caramel) To find the probability of getting candies with the indicated flavors, we first need to determine the total number of candies in the bowl. Total candies = 30 candies 10 (chocolate) + 8 (coffee) + 12 (caramel) GIVEN:
P(A) = P (chocolate) = P(B) = P (caramel) =
P ( A or B) = P(A) + P(B) Problem # 1 a. Probability of getting chocolate or caramel candy P (chocolate or caramel): P(A or B) = P(A) + P(B) P (chocolate or caramel) = P (chocolate) + P (caramel) = (^) + = ÷ Mutually exclusive events
Problem # 1 b. P (coffee or not caramel)
P(A) = P (coffee) = P(B) = P (not caramel) = Problem # 1 b. Probability of getting coffee or not caramel candy P (coffee or not caramel): Total candies = 30 candies 10 (chocolate) + 8 (coffee) + 12 (caramel) 10 + 8 = 18
Problem # 1 b. Probability of getting coffee or not caramel candy P (coffee or not caramel): Intersection 8 (coffee) P(A and B) = Not Mutually Exclusive Events P(A or B)= P(A) + P(B) - P(A and B)