4802Probability07 - Math 4802 Fall 2007 Probability...

Info iconThis preview shows page 1. Sign up to view the full content.

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

Unformatted text preview: Math 4802 Fall 2007 Probability Problems Due Tuesday, September 11: 1. Shuffle an ordinary deck of 52 playing cards, and then turn the cards face up one at a time. On average, how many cards are required to produce the first ace? 2. Show that the probability that December 25th falls on a Wednesday is not 1/7. (Leap years have 366 days; other years have 365 days. Year n is a leap year iff either (a) 4 divides n and 100 does not divide n, or (b) 400 divides n.) 3. Duels in the town of Putnamville are usually not fatal. Each contestant in a duel arrives at a random moment between 6AM and 7AM on the prescribed day, stays for 5 minutes, and then leaves, unless his opponent arrives within that 5-minute interval, in which case they fight to the death. What fraction of duels lead to casualties? 4. A drunken man standing one step from the edge of a cliff takes a sequence of random steps either away from or toward the cliff. At any step, his probability of taking a step away from the cliff is p (and therefore his probability of taking a step toward the cliff is 1 − p). What is the probability that the man will eventually fall off the cliff? 5. If α ∈ (0, 1) is irrational, prove that there is a finite game played with a fair coin such that the probability of one player winning the game is α. (A game is finite if with probability one it must end in a finite number of moves.) 6. A sequence of numbers αi ∈ [0, 1] is chosen at random with respect to the uniform distribution. Find the expected value of the unique integer n for which n−1 n αi ≤ 1 and i=1 i=1 αi > 1 . 1 ...
View Full Document

This note was uploaded on 03/13/2010 for the course MATH 4801 taught by Professor Staff during the Spring '08 term at Georgia Institute of Technology.

Ask a homework question - tutors are online