توضیح 1
Overlap: The intersection counted in both marginal probabilities.
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درس 4 از 16
Use general and special addition rules while distinguishing exclusivity from independence.
Theory
Use general and special addition rules while distinguishing exclusivity from independence.
توضیح 1
Overlap: The intersection counted in both marginal probabilities.
توضیح 2
Mutually exclusive: Events that cannot occur together.
توضیح 3
Collectively exhaustive: Events that cover the whole sample space.
اصطلاحات
The intersection counted in both marginal probabilities.
A loyalty member with a high-value cart.
Events that cannot occur together.
One order assigned exactly one priority.
Events that cover the whole sample space.
Low, medium, or high cart band.
نمادگذاری و فرمولها
P(A or B) = P(A) + P(B) - P(A and B)
Define every event before substituting values, then validate the result and denominator.
فعالیت تعاملی
P(A or B)
0.7
P(A) + P(B) - P(A and B)
The overlap is subtracted once because it was counted in both marginal probabilities.
مثال حلشده
سناریو
A review is triggered by a high cart or an unusual payment route.
Subtracting the overlap avoids double counting.
ارتباط با R
Run and edit the code, inspect intermediate output, and use the movable R Code Guide while practising.
Live R Lab
Calculate complements, unions, and intersections from original checkout events.
Ready to run
Dataset provenance
Original synthetic data generated for STATLAB Academy. No textbook data used.
Interpretation safeguard
Mutually exclusive events are generally not independent when both have positive probability.
بازاندیشی
Name the event, denominator, probability interpretation, and one operational limitation.
دستیار
Help me reason through Addition Rules and Event Structure by asking questions about my event definitions, denominator, formula choice, assumptions, and interpretation. Do not give a quiz answer before I submit.
ارزیابی پایانی
منبع
Explore additional probability explanations and exercises from properly licensed or publisher resources.
دریافتمنبع
Download an original worksheet or guide for this lesson.
دریافت