Math Problem Statement

An urn contains 8 white balls and 2 red balls. A second urn contains 3 white balls and 8 red balls. An urn is selected, and a ball is randomly drawn from the selected urn. The probability of selecting the first urn is 0.65. If the ball is white, find the probability that the second urn was selected. (Enter answer as a decimal with at least 4 correct decimal places)

Solution

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Math Problem Analysis

Mathematical Concepts

Probability
Conditional Probability
Bayes' Theorem

Formulas

P(A | B) = (P(B | A) * P(A)) / P(B)
P(B) = P(B | A_1) * P(A_1) + P(B | A_2) * P(A_2)

Theorems

Bayes' Theorem
Law of Total Probability

Suitable Grade Level

Grades 11-12 or College