Math Problem Statement

For a binomial distribution X~Bin(n,p), suppose n=5. If P(X=0)=0.00032, what is p? In your response, provide a detailed explanation of your steps and reasoning at each step.

Solution

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Math Problem Analysis

Mathematical Concepts

Binomial Distribution
Probability Theory
Algebra

Formulas

P(X = k) = \binom{n}{k} p^k (1 - p)^{n - k}
P(X = 0) = (1 - p)^n

Theorems

Binomial Theorem

Suitable Grade Level

Grades 10-12