Mathematics
Grade 11
15 min
Find probabilities using the addition rule
Find probabilities using the addition rule
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1
Introduction & Learning Objectives
Learning Objectives
Define mutually exclusive and non-mutually exclusive events.
State the Addition Rule for mutually exclusive events.
By the end of of this lesson, students will be able to state the General Addition Rule for non-mutually exclusive events.
Distinguish between scenarios requiring the simple versus the general addition rule.
Calculate the probability of the union of two events, P(A ∪ B).
Apply the addition rule to solve problems involving cards, dice, and data tables.
In a deck of cards, what are the chances you'll draw a Queen OR a Diamond? 🤔 The Addition Rule helps us solve exactly this kind of 'this OR that' puzzle!
This tutorial focuses on the Addition Rule of Probability, a fundamental tool for calculating the likelihood of one event OR...
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Key Concepts & Vocabulary
TermDefinitionExample
Sample Space (S)The set of all possible outcomes of a random experiment.For a single six-sided die roll, the sample space is S = {1, 2, 3, 4, 5, 6}.
EventA specific outcome or a set of outcomes from an experiment; a subset of the sample space.When rolling a die, the event 'rolling an even number' is the set {2, 4, 6}.
Union of Events (A ∪ B)The event that occurs if event A OR event B (or both) occurs. The key word is 'OR'.If A is rolling an even number {2, 4, 6} and B is rolling a number greater than 4 {5, 6}, then A ∪ B is {2, 4, 5, 6}.
Intersection of Events (A ∩ B)The event that occurs if both event A AND event B occur simultaneously. The key word is 'AND'.Using the events above, A ∩ B is {6}, since 6 is the only outcome that is both...
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Core Formulas
Addition Rule for Mutually Exclusive Events
P(A \cup B) = P(A) + P(B)
Use this rule when two events A and B cannot occur at the same time. Since there is no overlap, you simply add their individual probabilities.
General Addition Rule (for Non-Mutually Exclusive Events)
P(A \cup B) = P(A) + P(B) - P(A \cap B)
Use this rule for any two events. It accounts for events that can happen simultaneously by subtracting the probability of their intersection (the overlap) to avoid double-counting.
4 more steps in this tutorial
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Challenging
A student is told that two events, A and B, are mutually exclusive with P(A) = 0.2 and P(B) = 0.5. To find P(A ∪ B), they incorrectly calculate P(A) + P(B) - P(A)P(B). What is the fundamental error in the student's reasoning?
A.They used the wrong values for P(A) and P(B).
B.They confused the rule for mutually exclusive events with the rule for independent events.
C.They should have added P(A)P(B) instead of subtracting it.
D.They forgot to divide by the sample size.
Challenging
For two events A and B, it is known that P(A ∪ B) = 0.75, P(A ∩ B) = 0.15, and the events are equally likely, meaning P(A) = P(B). What is the value of P(B)?
A.0.60
B.0.30
C.0.45
D.0.90
Challenging
In a class of 80 students, 30 are on the soccer team, 25 are in the chess club, and 10 are in both. What is the probability that a randomly selected student is on the soccer team OR in the chess club, but NOT both?
A.9/16
B.1/8
C.11/16
D.7/16
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