Virginia SOL 8.PS.1.a
The Standard
Determine whether two events are independent or dependent and explain how replacement impacts the probability.
Virginia Standards of Learning for Mathematics · The student will use statistical investigation to determine the probability of independent and dependent events, including those in context.
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students decide whether one event changes the probability of another event. They compare situations with and without replacement and explain why the probabilities stay the same or change.
What Mastery Looks Like
- A student correctly labels event pairs as independent or dependent. They show how replacement keeps probabilities the same, while no replacement can change the probability of the next outcome.
Common Misconceptions
- Students may assume events are independent just because they happen one after another. They may also think replacement changes only the number of objects, not the probability of the second event.
How to Assess It
- Give this exit ticket: A bag has 3 red and 2 blue counters. Find the probability of drawing two reds with and without replacement, label each situation independent or dependent, and explain why.
Lesson moves
Ways to Teach It
Use a bag of colored tiles to compare two draws with replacement and without replacement, recording probabilities after each first draw.
Write an explanation: Why does replacing the first marble make the second draw independent of the first?
Sort event cards into independent or dependent pairs, then defend each choice using how the first event changes the second probability.
Compare quality checks that return a sampled product to a batch with checks that remove it before the next selection.
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Printable 8.PS.1.a Worksheet
A ready-to-print activity worksheet aligned to 8.PS.1.a, with an answer key for the teacher on its own page. No account needed.
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Related Standards
- 8.PS.1
The student will use statistical investigation to determine the probability of independent and dependent events, including those in context.
- 8.PS.1.c
Determine the probability of two independent events.
- 8.PS.1.b
Compare and contrast the probability of independent and dependent events.
- 8.PS.1.d
Determine the probability of two dependent events.
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