Probability and Statistics Practice Problems and Solutions
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Probability Fundamentals
- Mutually Exclusive Events: If A and B are mutually exclusive, then P(A ∪ B) ≠ 0.
- Independent Events: Events are independent if their probabilities match, such as P(A) = P(B) or P(A|B) = P(A).
- Conditional Probability Example: Find P(driver is age 65+ | driver is female) = P(driver is female and 65+) / P(driver is female).
- Key Formulas:
- P(S ∩ Y) = P(S ∩ Y) / Total
- P(S|Y) = P(S ∩ Y) / P(Y)
- P(Y ∪ S) = P(Y) + P(S) - P(Y ∩ S)
Probability Distributions
Expected Value Calculation
The payoff (X) for a lottery game has the following probability distribution. What is the expected value of X? (Hint: Find the value of 'a' first.)
Given values: 2 (0.4), 5 (0.3), 7 (0.2), 10 (a).
Calculation: 1 - (0.4 + 0.3 + 0.2) = 0.1, so a =... Continue reading "Probability and Statistics Practice Problems and Solutions" »