A frog starts at location A and wants to get to location B that is 500 meters away. Starting at A, it sits at a given spot on the path from A to B for a time that is exponen- tially distributed with parameter 1 (minute). After that, it jumps 1 meter towards

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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Question

A frog starts at location A and wants to get to location B that is 500 meters away.
Starting at A, it sits at a given spot on the path from A to B for a time that is exponen-
tially distributed with parameter 1 (minute). After that, it jumps 1 meter towards B, sits
in the new spot for an exponentially distributed time, etc. All the times are independent.
What is the probability (approximately) that it will get to B within 7 hours?

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