1. (2.5 pt.) A coin is flipped 10 times. Assume that all outcomes are equally likely. What is the probability that it lands on tails less than 4 times? 2. (2.5 pt.) A die is loaded so that rolling a 6 is two times as likely as rolling each of the other five numbers. What is the probability of rolling a number greater than 3 with this die? 3. (2.5 pt.) A bit string of length 4 is generated at random. Assume that all outcomes are equally likely. What is the probability that it contains an odd number of 0's given that its first bit is 0? 4. (2.5 pt.) A sports association decides to implement a drug screening procedure to test its athletes for illegal performance-enhancing drugs. A person who does not take the drugs will test positive with probability 0.02 and a person who does take the drugs will test negative with probability 0.04. Assume that 3% of the athletes take performance-enhancing drugs. What is the probability that an athlete testing positive actually takes the drugs?
1. (2.5 pt.) A coin is flipped 10 times. Assume that all outcomes are equally likely. What is the probability that it lands on tails less than 4 times? 2. (2.5 pt.) A die is loaded so that rolling a 6 is two times as likely as rolling each of the other five numbers. What is the probability of rolling a number greater than 3 with this die? 3. (2.5 pt.) A bit string of length 4 is generated at random. Assume that all outcomes are equally likely. What is the probability that it contains an odd number of 0's given that its first bit is 0? 4. (2.5 pt.) A sports association decides to implement a drug screening procedure to test its athletes for illegal performance-enhancing drugs. A person who does not take the drugs will test positive with probability 0.02 and a person who does take the drugs will test negative with probability 0.04. Assume that 3% of the athletes take performance-enhancing drugs. What is the probability that an athlete testing positive actually takes the drugs?
Operations Research : Applications and Algorithms
4th Edition
ISBN:9780534380588
Author:Wayne L. Winston
Publisher:Wayne L. Winston
Chapter12: Review Of Calculus And Probability
Section12.5: Random Variables, Mean, Variance, And Covariance
Problem 5P
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