Mathematics
Grade 11
15 min
Calculate probabilities of events
Calculate probabilities of events
What you'll learn
- Identify whether division facts for 2, 3, 4, 5, and 10 are true or false with 80% accuracy.
- Solve division problems involving facts for 2, 3, 4, 5, and 10 and determine if the given answer is correct in at least 4 out of 5 attempts.
- Explain why a division fact for 2, 3, 4, 5, or 10 is true or false using objects or drawings in at least 2 out of 3 instances.
- Apply knowledge of division facts for 2, 3, 4, 5, and 10 to determine if a given equation is true or false and provide a corrected equation if it is false in at least 3 out of 4 tries.
Tutorial Preview
1
Introduction & Learning Objectives
Learning Objectives
Define and calculate the theoretical probability of a single event.
Calculate the probability of the complement of an event using the complement rule.
Distinguish between mutually exclusive and non-mutually exclusive events and apply the appropriate Addition Rule to calculate their probabilities.
Distinguish between independent and dependent events and apply the appropriate Multiplication Rule.
Calculate conditional probabilities using the formula P(A|B) = P(A and B) / P(B).
Interpret and solve complex probability problems involving combined events from word problems or data tables.
What are the chances your favorite team wins the championship, or that you'll ace your next test? 🏆 Probability is the mathematics of chance!
This tutorial will move be...
2
Key Concepts & Vocabulary
TermDefinitionExample
Sample Space (S)The set of all possible outcomes of a random experiment.When rolling a standard six-sided die, the sample space is S = {1, 2, 3, 4, 5, 6}.
Event (E)A specific outcome or a set of outcomes from the sample space.When rolling a die, the event 'rolling an even number' is the set E = {2, 4, 6}.
Complement of an Event (E')The set of all outcomes in the sample space that are not in event E. It represents the event E not happening.If the event is 'rolling a 6' (E = {6}), the complement is 'not rolling a 6' (E' = {1, 2, 3, 4, 5}).
Mutually Exclusive EventsTwo or more events that cannot occur at the same time. They have no outcomes in common.When drawing one card from a deck, the events 'drawing a King' and ...
3
Core Formulas
The Complement Rule
P(A') = 1 - P(A)
The probability that an event A will not occur is 1 minus the probability that it will occur. This is useful for calculating the probability of 'at least one' of something happening.
The Addition Rule for Probability
P(A \cup B) = P(A) + P(B) - P(A \cap B)
Calculates the probability that event A OR event B (or both) will occur. If the events are mutually exclusive, P(A \cap B) = 0, and the formula simplifies to P(A \cup B) = P(A) + P(B).
The Multiplication Rule for Independent Events
P(A \cap B) = P(A) \times P(B)
Calculates the probability that two independent events, A AND B, will both occur. To use this, you must confirm the events are independent.
The Conditional Probability Formula
P(A|B) = \frac{P(A \cap...
4 more steps in this tutorial
Sign up free to access the complete tutorial with worked examples and practice.
Sign Up Free to ContinueSample Practice Questions
Challenging
If P(A|B) = 0.6 and P(B) = 0.3, what is the value of P(A ∩ B)?
A.0.5
B.2.0
C.0.9
D.0.18
Challenging
A factory has two machines, X and Y. Machine X produces 60% of the items, and Machine Y produces 40%. 2% of items from Machine X are defective, and 3% from Machine Y are defective. What is the probability that a randomly selected item is defective?
A.0.050
B.0.025
C.0.024
D.0.012
Challenging
Two events, A and B, are independent. If P(A) = 2x and P(B) = 3x, and P(A ∩ B) = 0.54, what is the value of x?
A.0.3
B.0.09
C.0.9
D.0.5
Want to practice and check your answers?
Sign up to access all questions with instant feedback, explanations, and progress tracking.
Start Practicing FreeMore from Probability
Mathematics for other grades
Frequently asked questions
What grade level is "Calculate probabilities of events"?
Calculate probabilities of events is a Grade 11 Mathematics lesson on ExcelOS.
What will I learn in Calculate probabilities of events?
You'll be able to: Identify whether division facts for 2, 3, 4, 5, and 10 are true or false with 80% accuracy; Solve division problems involving facts for 2, 3, 4, 5, and 10 and determine if the given answer is correct in at least 4 out of 5….
Is "Calculate probabilities of events" free to practice?
Yes. You can read the tutorial preview for free, and signing up for a free ExcelOS account unlocks the full tutorial and all practice questions with instant feedback.
How many practice questions are included with Calculate probabilities of events?
This lesson includes 25 practice questions across multiple difficulty levels, each with instant feedback and explanations.