Virginia SOL 8.PS.1.d
The Standard
Determine the probability of two dependent events.
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 find the chance of two events occurring when the first event changes the possible outcomes for the second. They multiply the first probability by the updated second probability.
What Mastery Looks Like
- A student updates both the favorable outcomes and total outcomes after the first event. The student multiplies the first probability by the conditional probability and simplifies the result.
Common Misconceptions
- Students may multiply using the original total for both draws, even when an item is not replaced. They may add probabilities instead of multiplying, or treat the order of events as irrelevant.
How to Assess It
- Give this exit ticket: “A bag has 4 red and 3 blue tiles. Two tiles are drawn without replacement. What is the probability both are red? Show each factor.”
Lesson moves
Ways to Teach It
Place colored counters in a bag, draw two without replacement, and compare experimental results with calculated probabilities.
Ask students to explain why the second probability changes when a card is drawn and not returned.
Play a card-pair challenge where teams calculate probabilities for two specified draws without replacement and earn points for correct reasoning.
Use a classroom prize box to calculate the chance of selecting two specific prize types when chosen items are not replaced.
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Printable 8.PS.1.d Worksheet
A ready-to-print activity worksheet aligned to 8.PS.1.d, with an answer key for the teacher on its own page. No account needed.
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Related Standards
- 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.
- 7.PS.1.a
Determine the theoretical probability of an event.
- 8.PS.1.a
Determine whether two events are independent or dependent and explain how replacement impacts the probability.
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