For Discrete Mathematics:

Problem 7 A wedding party of eight people is lined up in a random order. Every way of lining up the people in the wedding party is equally likely. (b) What is the probability that the maid of honor is in the leftmost position? Problem 8 A biased coin is flipped 10 times. In a single flip of the coin, the probability of heads is 1/3 and the probability of tails is 2/3. The outcomes of the coin flips are mutually independent. What is the probability of each event? (a) Every flip comes up heads. Problem 9 (a) Sally has two coins. The first coin is a fair coin and the second coin is biased. The biased coin comes up heads with probability .75 and tails with probability .25. She selects a coin at random and flips the coin ten times. The results of the coin flips are mutually independent. The result of the 10 flips is: T,T,H, T,H, T,T,T,H,T. What is the probability that she selected the biased coin? Problem 10 (a) The national flufferball association decides to implement a drug screening procedure to test its athletes for illegal performance enhancing drugs. 3% of the professional flufferball players actually use performance enhancing drugs. A test for the drugs has a false positive rate of 2% and a false negative rate of 4%. In other words, a person who does not take the drugs will test positive with probability 0.02. A person who does take the drugs will test negative with probability 0.04. A randomly selected player is tested and tests positive. What is the probability that she really does take performance enhancing drugs? Problem 11 (a) Assume one person out of 10,000 is infected with HIV, and there is a test in which 2.5% of all people test positive for the virus although they do not really have it. If you test negative on this test, then you definitely do not have HIV. What is the chance of having HIV, assuming you test positive for it