(A) Three marksmen fire simultaneously and independently at atarget. What is the probability of the target being hit at leastonce, given that marksman one hits a target nine times out of ten,marksman two hits a target eight times out of ten while marksmanthree only hits a target one out of every two times. (B) Fiftyteams compete in a student programming competition. It has beenobserved that 60% of the teams use the programming language C whilethe others use C++, and experience has shown that teams who programin C are twice as likely to win as those who use C++. Furthermore,ten teams who use C++ include a graduate student, while only fourof those who use C include a graduate student. (a) What is theprobability that the winning team programs in C? (b) What is theprobability that the winning team programs in C and includes agraduate student? (c) What is the probability that the winning teamincludes a graduate student? (d) Given that the winning teamincludes a graduate student, what is the probability that teamprogrammed in C? (C) A brand new light bulb is placed in a socketand the time it takes until it burns out is measured. Describe anappropriate sample space for this experiment. Use mathematical setnotation to describe the following events: (a) A = thelight bulblasts at least 100 hours. (b) B = thelight bulb lasts between 120and 160 hours. (c) C = thelight bulb lasts less than 200 hours. (D)A university professor drives from his home in Cary to hisuniversity office in Raleigh each day. His car, which is ratherold, fails to start one out of every eight times and he ends uptaking his wife’s car. Furthermore, the rate of growth of Cary isso high that traffic problems are common. The professor finds that70% of the time, traffic is so bad that he is forced to drive fasthis preferred exit off the beltline, Western Boulevard, and takethe next exit, Hillsborough street. What is the probability ofseeing this professor driving to his office along Hillsboroughstreet, in his wife’s car?
