You have 80 dollars and play the following game. An urn contains two white balls and two black balls. You draw the balls out one at a time without replacement until all the balls are gone. On each draw, you bet half of your present fortune that you will draw a white ball. If you do, you win an amount equal to your bet. If you do not, you lose your bet. What is your expected final fortune? Gerolamo Cardano in his book, The Gambling Scholar, written in the early 1500s, considers the following carnival game. There are six dice. Each of the dice has five blank sides. The sixth side has a number between 1 and 6--a different number on each die. The six dice are rolled and the player wins a prize depending on the total of the numbers which turn up. Find, as Cardano did, the expected total without finding its distribution.
You have 80 dollars and play the following game. An urn contains two white balls and two black balls. You draw the balls out one at a time without replacement until all the balls are gone. On each draw, you bet half of your present fortune that you will draw a white ball. If you do, you win an amount equal to your bet. If you do not, you lose your bet. What is your expected final fortune? Gerolamo Cardano in his book, The Gambling Scholar, written in the early 1500s, considers the following carnival game. There are six dice. Each of the dice has five blank sides. The sixth side has a number between 1 and 6--a different number on each die. The six dice are rolled and the player wins a prize depending on the total of the numbers which turn up. Find, as Cardano did, the expected total without finding its distribution.
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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Transcribed Image Text:You have 80 dollars and play the following game. An urn contains two white balls and two black balls. You
draw the balls out one at a time without replacement until all the balls are gone. On each draw, you bet
half of your present fortune that you will draw a white ball. If you do, you win an amount equal to your
bet. If you do not, you lose your bet. What is your expected final fortune?
Gerolamo Cardano in his book, The Gambling Scholar, written in the early 1500s, considers the following
carnival game. There are six dice. Each of the dice has five blank sides. The sixth side has a number
between 1 and 6--a different number on each die. The six dice are rolled and the player wins a prize
depending on the total of the numbers which turn up. Find, as Cardano did, the expected total without
finding its distribution.
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