Probability
▶︎ Watch it animatedinteractive step-through · ~3 min · optionalA probability is favorable over total for one named event, and every trap here bends one of those three words. The points leak in the denominator, a condition ignored or applied to the wrong group, in the operation, both-and added or either-or multiplied or at-least-one taken head-on, and at the end, in the event: the complement, a raw count, or the odds reported instead.
These patterns aren't really about whether you can form a fraction. They're about whether the if-clause shrank your denominator, whether the structure of the event picked the operation, and whether the number you reported is the probability of the exact event the question named.
The work
4 ways in · any order
Lesson
Probability
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Let each condition set the denominator, multiply for independent AND and add for exclusive OR, take at-least-one through the complement, and shrink the pool when draws are not replaced. The lesson works the method and the three patterns that derail it, and it saves the trap for last: the complement handed in for the event.
Diagnostic
10-item topic check
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Ten items across the three patterns: conditional probability over the wrong group, the wrong operation combining events, and the complement or count reported. A mix of two-way tables, spinners, draws with and without replacement, and expected counts. Take it cold to surface the ones still catching you, or after the lesson to confirm they are gone.
Grid-in Check
Student-produced response
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About a quarter of SAT math answers are typed, not chosen, with no options to react to. These grid-in items diagnose by the value you enter, then route into the same drills the multiple-choice check feeds.
Targeted Practice
Drill a single pattern
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Pick one of the failure modes you've missed and grind it on its own. The round is adaptive: two correct in a row clears the pattern and you move on.