## Math Problem Statement

## Solution

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## Math Problem Analysis

### Mathematical Concepts

Probability

Binomial Distribution

Expected Value

Standard Deviation

### Formulas

Complement Rule: P(one or more) = 1 - P(none)

P(two or more) = 1 - (P(x = 0) + P(x = 1))

P(three or more) = 1 - (P(x = 0) + P(x = 1) + P(x = 2))

Expected value: μ = Σ[x * P(x)]

Standard deviation: σ = √[Σ(x^2 * P(x)) - μ^2]

### Theorems

Law of Total Probability

Properties of Expected Value

Properties of Variance and Standard Deviation

### Suitable Grade Level

College / University Level

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