math 411 homework4

# math 411 homework4 - numbers will appear at least once?...

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Department of Mathematics Fall 2011 Volodymyr Nekrashevych Math 411 — Problem Set 4 Issued: 09.23 Due: training 4.1. If we ﬂip a coin 5 times, what is the probability that the number of heads is an even number? 4.2. Three students each have probability 1 / 3 of solving a problem. What is the probability that at least one of them will solve the problem? We assume that the two events (students solving the problem) are independent. 4.3. Three dice are rolled. For a \$1 bet you win \$1 for each 6 that appears (plus your dollar back). If no 6 appears you lose your dollar. What is the expected value of your win? 4.4. Suppose we roll two tetrahedral dice that have 1 , 2 , 3, and 4 on their four sides. Find the distribution for the sum of the three numbers. 4.5. A random variable has P ( X = x ) = x/ 15 for x ∈ { 1 , 2 , 3 , 4 , 5 } , and 0 otherwise. Find the mean and variance of X . 4.6. If seven dice are rolled, what is the probability that each of the six

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Unformatted text preview: numbers will appear at least once? 4.7. What is the probability of guessing exactly 3 out of 5 multiple choice questions, if each question has four answers? 4.8. Calls to a toll-free hotline service are made randomly at rate 2 per minute. The service has ve operators, none of whom is currently busy. Use the Poisson distribution to estimate the probability that in the next ve minute there are less than ve calls. 4.9. You pick ve cards out of a deck of 52. What is the probability that you get exactly 2 spades? 4.10. A drawer contains 10 black, 8 brown, and 6 blue socks. If we pick two socks at random, what is the probability that they match? 4.11. You pick 13 cards out of a deck of 52. What is the probability that you will not get a card from every suit? (Use the inclusion-exclusion formula.)...
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## This note was uploaded on 02/13/2012 for the course MATH 411 taught by Professor Staff during the Fall '08 term at Texas A&M.

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math 411 homework4 - numbers will appear at least once?...

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