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AMU MATH 120 Week 3 Probability Fundamentals

Master probability rules, conditional probability, and counting techniques

Week 3 Probability Concepts

Week 3 introduces probability theory, covering basic probability concepts, conditional probability, the multiplication rule, the addition rule for mutually exclusive and non-mutually exclusive events, and counting techniques using permutations and combinations. You'll learn to calculate probabilities for real-world scenarios like quality control, risk assessment, and decision-making under uncertainty.

Where Students Struggle

Common mistakes include confusing independent and dependent events, forgetting to check for mutual exclusivity before applying the addition rule, and mixing up permutation and combination formulas. Another challenge is determining when to multiply probabilities versus when to add them. Our guides include decision trees for choosing the correct probability rule and worked examples for every scenario type.

Week 3 Help Resources

You receive complete solutions for MyStatLab Homework 3, probability rule flowcharts, permutation vs combination decision guides, and forum posts connecting probability to insurance, gambling, and quality control applications. We provide practice problems that build intuition for when events are independent versus dependent and when order matters in counting problems.

Frequently Asked Questions

❓How do I know when to multiply vs add probabilities?

Multiply probabilities when finding the probability that multiple events ALL occur (using AND). Add probabilities when finding the probability that AT LEAST ONE event occurs (using OR). For example, P(A and B) uses multiplication; P(A or B) uses addition. Always check if events are independent and mutually exclusive first.

❓What's the difference between permutations and combinations?

Permutations count arrangements where order matters (like race rankings or passwords). Combinations count selections where order doesn't matter (like committee members or lottery numbers). Use permutations when the problem asks about arrangements, sequences, or order. Use combinations when it asks about groups, selections, or committees.

❓How do I calculate conditional probability?

Conditional probability P(A|B) means 'probability of A given that B has occurred.' Use the formula P(A|B) = P(A and B) / P(B). This restricts the sample space to only outcomes where B occurred. MyStatLab's Help Me Solve This walks through conditional probability step-by-step for each problem type.

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