Florida B.E.S.T. MA.912.DP.4.4

MathGrades 9–12Use and interpret independence and probability.

The Standard

Interpret the independence of two events using conditional probability.

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

Teacher's field guide

What Students Need to Do: Students find the chance of one event among cases where another event happened. They compare that result with the overall chance to decide whether the events affect each other.
What Mastery Looks Like: Students correctly calculate a conditional probability from a table, diagram, or situation. They compare it with the overall probability and explain whether one event changes the likelihood of the other.
Common Misconceptions: Students often confuse independent events with mutually exclusive events. They may assume events are independent because they sound unrelated. They also use the full sample as the denominator when finding a conditional probability.
How to Assess It: Exit ticket: Of 100 students, 40 play a sport, 30 join a club, and 12 do both. Decide whether the events are independent and justify with probabilities.

Lesson moves

Draw two cards with and without replacement, record results, and compare the chance of a red second card after a red first card.
Ask students to explain why mutually exclusive events with positive probabilities cannot be independent.
Give pairs two-way table cards to sort as independent or dependent, then require a probability calculation for each choice.
Use school attendance and bus-rider data to test whether riding the bus is independent of arriving late.

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