Math Problem Statement
The contents of urns I, II and III are as follows: 1 4h67, 2 89:;< := 3 0 8:99>, 2 4h67, 1 89:;< := 1 0 8:99>, 4 4h67, 5 89:;< := 3 0 8:99>. Once urn is chosen at random and one ball is drawn. It happened to be white. What is the probability that it came from urn II? (b) What is the expected number of heads appearing when a fair coin is tossed three times? (c) Find the parameters (= and ?), of a binomial distribution which has mean equal to 6
Solution
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Math Problem Analysis
Mathematical Concepts
Probability
Expected Value
Binomial Distribution
Formulas
Bayes' Theorem: P(Urn II | White Ball) = [P(White Ball | Urn II) * P(Urn II)] / P(White Ball)
Expected Value for Binomial Distribution: E(X) = n * p
Mean of Binomial Distribution: μ = n * p
Variance of Binomial Distribution: σ² = n * p * (1 - p)
Theorems
Bayes' Theorem
Binomial Theorem
Suitable Grade Level
Grades 10-12
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