Florida B.E.S.T. MA.912.DP.4.8
The Standard
Apply the general multiplication rule for probability, taking into consideration whether the events are independent, and interpret the result in terms of the context.
Florida B.E.S.T. Standards for Mathematics
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students find the probability that two events both happen. They use a conditional probability when the first event affects the second, and ordinary multiplication when the events are independent. They explain what the result means in context.
What Mastery Looks Like
- Students choose the correct second probability based on what happened first. They calculate the probability that both events occur and explain the answer using the situation and an expected frequency.
Common Misconceptions
- Students may multiply two unconditional probabilities even when the first event changes the second. They may confuse independent events with mutually exclusive events. They also overlook whether an item is replaced before the next selection.
How to Assess It
- Exit ticket: A bag has 3 red and 2 blue tiles. Find the probability of drawing two red tiles without replacement, identify whether the events are independent, and interpret the result for 100 trials.
Lesson moves
Ways to Teach It
Have pairs draw colored tiles with and without replacement, record outcomes, and compare calculated probabilities with experimental results.
Ask students to explain why multiplying two original probabilities fails when the first event changes the sample space.
Give teams event cards to sort as independent or dependent, then award points for correct joint probability calculations.
Given that 8% of students are absent and 30% of absent students miss a quiz, calculate and interpret the probability of both.
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Related Standards
- MA.912.DP.4.9
Apply the addition and multiplication rules for counting to solve mathematical and real-world problems, including problems involving probability.
- MA.912.DP.4.3
Calculate the conditional probability of two events and interpret the result in terms of its context.
- MA.912.DP.4.7
Apply the addition rule for probability, taking into consideration whether the events are mutually exclusive, and interpret the result in terms of the model and...
- MA.912.DP.4.2
Determine if events A and B are independent by calculating the product of their probabilities.
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