Math Problem Statement

A set of math problems involving probability, combinatorics, and independence of events. Specific questions include divisibility, biased dice, probability of truth-telling, equipment failure, and solving problems with different probabilities of success.

Solution

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Math Problem Analysis

Mathematical Concepts

Probability theory
Independence of events
Combinatorics
Bayesian probability

Formulas

P(A ∩ B) = P(A) * P(B) for independent events
P(A ∪ B) = P(A) + P(B) - P(A ∩ B)
Binomial probabilities

Theorems

Law of total probability
Independence of events

Suitable Grade Level

Undergraduate Level or Advanced High School

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