Mathematics
Grade 7
15 min
Identify independent and dependent events
Identify independent and dependent events
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Introduction & Learning Objectives
Learning Objectives
Define 'event' and 'outcome' in the context of probability.
Distinguish between independent and dependent events.
Provide real-world examples of both independent and dependent events.
Analyze a given scenario to determine if events are independent or dependent.
Explain why the outcome of one event might or might not affect the probability of another event.
Have you ever wondered if one action you take affects the chances of something else happening? 🤔 Let's explore how events can be connected!
In this lesson, you'll learn to identify whether two events are independent or dependent. Understanding this difference is crucial for predicting outcomes and making sense of probability in everyday situations, from games to weather for...
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Key Concepts & Vocabulary
TermDefinitionExample
EventAn event is a specific outcome or a set of outcomes in a probability experiment.When rolling a standard die, 'rolling a 3' is an event. 'Rolling an even number' is also an event.
OutcomeAn outcome is a single possible result of a probability experiment.When flipping a coin, 'heads' is an outcome, and 'tails' is another outcome.
ProbabilityProbability is the measure of how likely an event is to occur, expressed as a number between 0 and 1 (or 0% and 100%).The probability of flipping a coin and getting heads is $\frac{1}{2}$ or 50%.
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, then flipping it again...
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Core Formulas
Rule for Identifying Independent Events
If Event A occurs, the probability of Event B occurring remains the same.
To determine if two events are independent, ask yourself: 'Does what happened in the first event change the possible outcomes or the likelihood of the second event?' If the answer is no, they are independent. For example, $P(B \text{ after } A) = P(B)$.
Rule for Identifying Dependent Events
If Event A occurs, the probability of Event B occurring changes.
To determine if two events are dependent, ask yourself: 'Does what happened in the first event change the possible outcomes or the likelihood of the second event?' If the answer is yes, they are dependent. For example, $P(B \text{ after } A) \neq P(B)$.
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Challenging
You have two bags. Bag A has 3 red and 2 blue marbles. Bag B has 2 red and 3 blue marbles. You flip a coin. If it's heads, you draw a marble from Bag A. If it's tails, you draw from Bag B. Are the event 'coin is heads' and the event 'marble is red' independent or dependent?
A.Independent, because the coin flip and marble draw are separate actions.
B.Dependent, because the outcome of the coin flip determines which bag you draw from, which in turn affects the probability of drawing a red marble.
C.Independent, because both bags contain red marbles.
D.Dependent, because there are two bags.
Challenging
A friend claims: 'If two events are dependent, the first event must happen before the second event.' Which statement best evaluates this claim?
A.The claim is correct. Dependency is defined by the order of events.
B.The claim is incorrect. Two events can be dependent even if they happen at the same time, for example, drawing two cards from a deck simultaneously.
C.The claim is correct. Independent events can happen in any order, but dependent events must be sequential.
D.The claim is incorrect. The order of events has nothing to do with probability.
Challenging
Event A is 'it is cloudy in the morning'. Event B is 'the afternoon baseball game is canceled'. How are these events related?
A.They are independent because the weather cannot be controlled.
B.They are dependent because the presence of clouds in the morning increases the probability of rain later, which in turn increases the probability of the game being canceled.
C.They are independent because a cloudy morning does not guarantee an afternoon cancellation.
D.They are dependent only if it actually rains.
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