Mathematics
Grade 9
15 min
Probabilities of compound events
Probabilities of compound events
What you'll learn
- Identify and state the five triangle congruence postulates (SSS, SAS, ASA, AAS, HL) with 100% accuracy when given a diagram or written description.
- Apply the triangle congruence postulates (SSS, SAS, ASA, AAS, HL) to construct logical two-column proofs demonstrating that two triangles are congruent, achieving a minimum score of 80% on a formative assessment.
- Explain the relationship between congruent triangles and corresponding parts (CPCTC) and use CPCTC to prove that corresponding sides or angles of congruent triangles are congruent, with at least 75% accuracy on problem-solving tasks.
- Analyze a given geometric diagram and determine the necessary steps and congruence postulates needed to prove a specific statement about the triangles or their parts, justifying each step in a two-column proof with clear and concise reasoning in at least three out of four attempts.
- Analyze a complex geometric diagram to determine which congruence postulate or theorem is most efficient to use in proving triangle congruence, and justify their choice using precise mathematical language in a short written response.
Tutorial Preview
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Introduction & Learning Objectives
Learning Objectives
Define compound events, independent events, dependent events, mutually exclusive events, and inclusive events.
Differentiate between independent and dependent events in a given scenario.
Distinguish between mutually exclusive and inclusive events.
Calculate the probability of two independent events occurring using the multiplication rule.
Calculate the probability of two dependent events occurring.
Calculate the probability of 'A or B' for both mutually exclusive and inclusive events using the appropriate addition rules.
Solve word problems involving compound events by selecting and applying the correct formula.
What are the chances of you rolling doubles in a board game AND your opponent landing on your property? 🎲 Let's find out!
This...
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Key Concepts & Vocabulary
TermDefinitionExample
Compound EventAn event that consists of two or more simple events. These events can be linked with words like 'and' or 'or'.Rolling a 4 on a die AND flipping a tail on a coin.
Independent EventsTwo events where the outcome of one event does not affect the probability or outcome of the other event.Flipping a coin twice. The result of the first flip has no impact on the result of the second flip.
Dependent EventsTwo events where the outcome of the first event changes the probability of the second event.Drawing a card from a deck, NOT replacing it, and then drawing a second card. The first draw changes the cards available for the second draw.
Mutually Exclusive EventsTwo events that cannot happen at the same time. They have no outcomes in common.When...
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Core Formulas
Multiplication Rule for Independent Events
P(A \text{ and } B) = P(A) \times P(B)
Use this rule when you want to find the probability of two independent events both happening. You multiply their individual probabilities.
Multiplication Rule for Dependent Events
P(A \text{ and } B) = P(A) \times P(B|A)
Use this for dependent events. P(B|A) means 'the probability of B happening, given that A has already happened'. The probability of the second event is adjusted based on the first event's outcome.
Addition Rule for Mutually Exclusive Events
P(A \text{ or } B) = P(A) + P(B)
Use this when you want to find the probability of one event OR another mutually exclusive event happening. You simply add their probabilities.
General Addition Rule for Inclusive Ev...
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Challenging
You roll a standard six-sided die and draw one card from a standard 52-card deck. What is the probability that you roll an even number OR you draw a face card (Jack, Queen, or King)?
A.1/2 + 12/52
B.1/2 + 12/52 - (1/2 × 12/52)
C.1/2 × 12/52
D.1 - (1/2 × 12/52)
Challenging
The probability of a fair coin landing on heads AND a special spinner landing on its single 'Win' section is 1/14. If the spinner has equal sections, how many total sections does it have?
A.7
B.14
C.12
D.28
Challenging
You flip a fair coin 3 times. What is the probability of getting at least one tail?
A.1/8
B.3/8
C.1/2
D.7/8
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Frequently asked questions
What grade level is "Probabilities of compound events"?
Probabilities of compound events is a Grade 9 Mathematics lesson on ExcelOS.
What will I learn in Probabilities of compound events?
You'll be able to: Identify and state the five triangle congruence postulates (SSS, SAS, ASA, AAS, HL) with 100% accuracy when given a diagram or written description; Apply the triangle congruence postulates (SSS, SAS, ASA, AAS, HL) to construct….
Is "Probabilities of compound 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 Probabilities of compound events?
This lesson includes 25 practice questions across multiple difficulty levels, each with instant feedback and explanations.