Math Problem Statement

find final answer for each part, check your answer 5 times to check if its 100% right before giving to me

Solution

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Math Problem Analysis

Mathematical Concepts

Probability
Binomial Distribution
Statistics
Expected Value
Standard Deviation

Formulas

Expected value for binomial distribution: E[X] = n * p
Standard deviation for binomial distribution: σ[X] = sqrt(n * p * (1 - p))
Binomial probability mass function: P(X = k) = (n choose k) * p^k * (1-p)^(n-k)

Theorems

Law of Large Numbers
Central Limit Theorem (implicitly relevant for cumulative probabilities)

Suitable Grade Level

Grades 11-12 or College