Mathematics
Grade 11
15 min
Probability of independent and dependent events
Probability of independent and dependent events
What you'll learn
- Identify whether a division sentence (up to 10 ÷ whole numbers resulting in whole numbers) is true or false with 80% accuracy.
- Solve division problems (up to 10 ÷ whole numbers resulting in whole numbers) to determine if a given division sentence is true or false.
- Explain why a division sentence (up to 10 ÷ whole numbers resulting in whole numbers) is true or false using manipulatives or drawings.
- Apply their understanding of division to create one true and one false division sentence (up to 10 ÷ whole numbers resulting in whole numbers).
Tutorial Preview
1
Introduction & Learning Objectives
Learning Objectives
Define and differentiate between independent and dependent events.
Calculate the probability of two or more independent events occurring using the multiplication rule.
Define conditional probability and its notation, P(B|A).
Calculate the probability of two or more dependent events occurring using the general multiplication rule.
Use the probability test P(A and B) = P(A) * P(B) to determine if two events are independent.
Apply the concepts of independent and dependent probability to solve multi-step, real-world problems.
If you draw a King from a deck of cards and don't put it back, does that change your odds of drawing another King? 👑 Let's find out!
This tutorial explores how the outcome of one event can sometimes affect the probability of...
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Key Concepts & Vocabulary
TermDefinitionExample
Independent EventsTwo events are independent if the occurrence of one event does not affect the probability of the other event occurring.Flipping a coin and getting 'heads', and then rolling a standard six-sided die and getting a '5'. The coin flip has no impact on the die roll.
Dependent EventsTwo events are dependent if the occurrence of the first event changes the probability of the second event occurring.Drawing a card from a deck and not replacing it, then drawing a second card. The first draw changes the composition of the deck for the second draw.
Conditional ProbabilityThe probability of an event (B) occurring, given that another event (A) has already occurred. It is denoted as P(B|A), read as 'the probability of B given A'.The p...
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Core Formulas
Multiplication Rule for Independent Events
P(A \text{ and } B) = P(A) \times P(B)
Use this rule to find the probability of two independent events both occurring. You simply multiply their individual probabilities.
General Multiplication Rule (for Dependent Events)
P(A \text{ and } B) = P(A) \times P(B|A)
Use this rule to find the probability of two dependent events both occurring. You multiply the probability of the first event by the conditional probability of the second event, given the first has occurred.
Test for Independence
\text{Events A and B are independent if and only if } P(A \text{ and } B) = P(A) \times P(B)
This is a formal test to check for independence. If the probability of both events happening together equals the product of their individual probabi...
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Challenging
Events A and B are independent. The probability of event A is 'x' and the probability of event B is 'x + 0.2'. If the probability of both A and B occurring is 0.15, what is the value of x?
A.0.5
B.0.25
C.0.3
D.0.1
Challenging
Three letters are chosen one by one without replacement from the word 'SEQUENCES'. What is the probability that the selection is a consonant, then a vowel, then another consonant?
A.5/18
B.20/81
C.1/9
D.5/42
Challenging
In a survey, it was found that 60% of people own a car (Event A), and 30% of people own a motorcycle (Event B). If owning a car and owning a motorcycle are independent events, what is the probability that a randomly selected person owns NEITHER a car NOR a motorcycle?
A.10%
B.18%
C.40%
D.28%
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Frequently asked questions
What grade level is "Probability of independent and dependent events"?
Probability of independent and dependent events is a Grade 11 Mathematics lesson on ExcelOS.
What will I learn in Probability of independent and dependent events?
You'll be able to: Identify whether a division sentence (up to 10 ÷ whole numbers resulting in whole numbers) is true or false with 80% accuracy; Solve division problems (up to 10 ÷ whole numbers resulting in whole numbers) to determine if a given….
Is "Probability of independent and dependent events" free to practice?
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How many practice questions are included with Probability of independent and dependent events?
This lesson includes 25 practice questions across multiple difficulty levels, each with instant feedback and explanations.