Math Problem Statement
A utility company might offer electrical rates based on time-of-day consumption to decrease the peak demand in a day. Enough customers need to accept the plan for it to be successful. Suppose that among 50 major customers, 15 would accept the plan. The utility selects 10 major customers randomly (without replacement) to contact and promote the plan. (a) What is the probability that exactly two of the selected major customers accept the plan? (b) What is the probability that at least one of the selected major customers accepts the plan?
Solution
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Math Problem Analysis
Mathematical Concepts
Statistics
Probability Theory
Hypergeometric Distribution
Formulas
P(X = k) = (C(K, k) * C(N - K, n - k)) / C(N, n)
P(X ≥ 1) = 1 - P(X = 0)
Theorems
Hypergeometric Distribution
Suitable Grade Level
Undergraduate
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