MIT6_042JS10_lec39_sol

MIT6_042JS10_lec39_sol - Massachusetts Institute of...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Massachusetts Institute of Technology 6.042J/18.062J, Spring ’10 : Mathematics for Computer Science May 12 Prof. Albert R. Meyer revised May 10, 2010, 678 minutes Solutions to In-Class Problems Week 14, Wed. Problem 1. A gambler is placing $1 bets on the “1st dozen” in roulette. This bet wins when a number from one to twelve comes in, and then the gambler gets his $1 back plus $3 more. Recall that there are 38 numbers on the roulette wheel. The gambler’s initial stake in $ n and his target is $ T . He will keep betting until he runs out of money (“goes broke”) or reachs his target. Let w n be the probability of the gambler winning, that is, reaching target $ T before going broke. (a) Write a linear recurrence for w n ; you need not solve the recurrence. Solution. The probability of winning a bet is 12 / 38 . Thus, by the Law of Total Probability ?? , w n = Pr { win starting with $ n | won first bet } · Pr { won first bet } + Pr { win starting with $ n | lost first bet } · Pr = Pr { win starting with $ n + 3 } · Pr { won first bet } + Pr { win starting with $...
View Full Document

This note was uploaded on 05/27/2011 for the course CS 6.042J taught by Professor Prof.albertr.meyer during the Spring '11 term at MIT.

Page1 / 4

MIT6_042JS10_lec39_sol - Massachusetts Institute of...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online