There is treasure in a lake with probability 1/2 . Each time you dive, the prob- ability is 1/3 that you will find treasure, if treasure is there, regardless of how many times you have dived previously. The treasure is worth $12,000. It costs $1,000 to make a dive. (1) You decide to make at least one dive. What is the expected value of your first dive? (The expected gain minus the expected cost.) (2) Suppose you dive once without finding treasure. What is the expected value of diving a second time? (Do not count the cost of the first dive.) (3) You decide to dive until the expected value of an addi- tional dive is negative. What is the maximum number of dives you will make, what is the expected value from following your strategy, and why does your strategy maximize expected value?

There is treasure in a lake with probability 1/2 . Each time you dive, the prob- ability is 1/3 that you will find treasure, if treasure is there, regardless of how many times you have dived previously. The treasure is worth $12,000. It costs $1,000 to make a dive. (1) You decide to make at least one dive. What is the expected value of your first dive? (The expected gain minus the expected cost.) (2) Suppose you dive once without finding treasure. What is the expected value of diving a second time? (Do not count the cost of the first dive.) (3) You decide to dive until the expected value of an addi- tional dive is negative. What is the maximum number of dives you will make, what is the expected value from following your strategy, and why does your strategy maximize expected value?

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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