DATA 140 MIDTERM Practice Questions with Complete Solutions (Latest 2025) Exponential Approximation - Correct Answers ✅log both sides log(1+x) ~ x solve for P ~ e Addition Rule - Correct Answers ✅if A&B are mutually exclusive events, P(AB) = P(A) + P(B) Difference Rule - Correct Answers ✅If B is a subset of A, P(A not B) = P(A)-P(B) Complement Rule - Correct Answers ✅P(A^c) = 1 - P(A) Conditional Probability / Bayes Rule - Correct Answers
✅P(A|B) = P(AB)/P(B) = P(A)P(B|A) / P(B)
Multiplication Rule- Independent Events - Correct Answers
✅P(AB) = P(A) * P(B)
Multiplication Rule- Dependent Events - Correct Answers
✅P(AB) = P(A)*P(B|A)
P(AB)=P(B)*P(A|B)
RV-Equality - Correct Answers ✅2 RVs are equal if their values are the same for every outcome 1 / 2
DATA 140 MIDTERM Practice Questions with Complete Solutions (Latest 2025) Inclusion-Exclusion (for unions) - Correct Answers ✅P(A or
B) = P(A) + P(B) - P(AB)
Union of a collection - Correct Answers ✅event that at least one occurs
1. Addition Rule: if mutually exclusive
2. Inclusion-Exclusion: if you know P(AB)
- Boole's Inequality --> bound
Complement of the union - Correct Answers ✅event that none of them occurs Boole's Inequality - Correct Answers ✅upper bound on the chance of the union of n events. the chance that at least one of the events occurs can be no larger than the sum of the chances.--> bound when you don't know dependence ex: chance of rain sat 40%, sun 10%:
chance of rain one of the days: 40% <= rain <= 50%
P(no match)= - Correct Answers ✅1-P(at least 1 match) Simple Random Sample (SRS) - Correct Answers ✅sample drawn at random without replacement from a finite pop.
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