19. An urn contains n red and m blue balls. They are withdrawn one at a time until a total of r,r ≤n, red balls have been withdrawn. Find the probability that a total of k balls are withdrawn. Hint: A total of k balls will be withdrawn if there are r 1 red balls in the first k-1 withdrawals and the kth withdrawal is a red ball. 00

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.8: Probability
Problem 32E
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How can I find the probability that a total of k balls are withdrawn? 

19. An urn contains \(n\) red and \(m\) blue balls. They are withdrawn one at a time until a total of \(r, r \leq n,\) red balls have been withdrawn. Find the probability that a total of \(k\) balls are withdrawn.

**Hint:** A total of \(k\) balls will be withdrawn if there are \(r - 1\) red balls in the first \(k - 1\) withdrawals and the \(k\)th withdrawal is a red ball.
Transcribed Image Text:19. An urn contains \(n\) red and \(m\) blue balls. They are withdrawn one at a time until a total of \(r, r \leq n,\) red balls have been withdrawn. Find the probability that a total of \(k\) balls are withdrawn. **Hint:** A total of \(k\) balls will be withdrawn if there are \(r - 1\) red balls in the first \(k - 1\) withdrawals and the \(k\)th withdrawal is a red ball.
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