Math Problem Statement
Two boxes contain respectively 3 red, 2 black balls and bred, 8 black balls. A fair coin is tossed. A ball is to be drawn from any of these boxes according to the toss of the coin. If the coin shows head a ball is taken from the first box and if the coin shows tail a ball is taken from box 2. Finally a red ball was chosen. Find the probability that coin was resulted in head.
Solution
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Math Problem Analysis
Mathematical Concepts
Conditional Probability
Bayes' Theorem
Formulas
Bayes' Theorem: P(A | B) = [P(B | A) * P(A)] / P(B)
Total Probability: P(B) = P(B | A1) * P(A1) + P(B | A2) * P(A2)
Theorems
Bayes' Theorem
Suitable Grade Level
Grades 10-12
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