3.9.5 At time 0, a blood culture starts with one red cell. At the end of 1 min, the red cell dies and is replaced by one of the following combinations with the probabilities as indicated: Two red cells One red, One white Two white Each red cell lives for 1 min and gives birth to offspring in the same way as the parent cell. Each white cell lives for 1 min and dies without reproducing.

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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3.9.5 At time 0, a blood culture starts with one red cell. At the end of 1 min, the
red cell dies and is replaced by one of the following combinations with the
probabilities as indicated:
Two red cells
One red, One white
Two white
a leo
12
Each red cell lives for 1 min and gives birth to offspring in the same way as
the parent cell. Each white cell lives for 1 min and dies without reproducing.
Assume that individual cells behave independently.
(a) At time n+min after the culture begins, what is the probability that no
white cells have yet appeared?
(b) What is the probability that the entire culture eventually dies out entirely?
Transcribed Image Text:3.9.5 At time 0, a blood culture starts with one red cell. At the end of 1 min, the red cell dies and is replaced by one of the following combinations with the probabilities as indicated: Two red cells One red, One white Two white a leo 12 Each red cell lives for 1 min and gives birth to offspring in the same way as the parent cell. Each white cell lives for 1 min and dies without reproducing. Assume that individual cells behave independently. (a) At time n+min after the culture begins, what is the probability that no white cells have yet appeared? (b) What is the probability that the entire culture eventually dies out entirely?
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