Florida B.E.S.T. MA.912.DP.4.2

MathGrades 9–12Use and interpret independence and probability.

The Standard

Determine if events A and B are independent by calculating the product of their probabilities.

Florida B.E.S.T. Standards for Mathematics

Teacher's field guide

What Students Need to Do: Students multiply the probabilities of two events and compare the result with the probability that both occur. A match shows independence, while a mismatch shows dependence.
What Mastery Looks Like: Students correctly find the individual and joint probabilities from given data. They compare P(A)P(B) with P(A and B), state whether the events are independent, and support the decision with numbers.
Common Misconceptions: Students often confuse independent events with mutually exclusive events. They may compare the product to P(A or B), or assume unrelated-sounding events are automatically independent.
How to Assess It: Give this exit ticket: P(A) = 0.4, P(B) = 0.5, and P(A and B) = 0.18. Show the needed calculation and decide whether the events are independent.

Lesson moves

Flip a coin and roll a die 60 times, then tally heads, even rolls, and outcomes where both occur to test independence.
Ask students to explain why mutually exclusive events with positive probabilities cannot be independent, using a numerical example.
Give pairs of probability cards and have teams sort them into independent or dependent groups by checking the product rule.
Use a two-way table of customers buying coffee and pastries to decide whether the two purchases appear independent.

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