Math Problem Statement
Suppose a box A contains 4 green and 5 black coins and box B contains 6 green and 3 black coins. A coin is chosen at random from box A and placed in box B.Finally,a coin is chosen at random from among those now in box B. What is the probability a blue coin was transferred from box A to box B given that the coin from box B is green?
Solution
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Math Problem Analysis
Mathematical Concepts
Probability
Conditional Probability
Bayes' Theorem
Formulas
P(G_A \mid G_B) = \frac{P(G_B \mid G_A) \cdot P(G_A)}{P(G_B)}
P(G_A) = \frac{4}{9}
P(G_B \mid G_A) = \frac{7}{10}
P(G_B) = P(G_B \mid G_A) \cdot P(G_A) + P(G_B \mid \neg G_A) \cdot P(\neg G_A)
Theorems
Bayes' Theorem
Suitable Grade Level
High School (Grades 9-12)
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