| [ QuizWit ] in KIDS 글 쓴 이(By): iLUSiON (띠띠빤쮸) 날 짜 (Date): 2005년 12월 19일 월요일 오전 04시 39분 38초 제 목(Title): probability quiz my class had final exam today.. damn cold... let's see who can solve this problem. a girl in my calss solved this using really crazy method. i am impressed. ^^ these two problems are hard.. other problems are trivial. ^^ PROBLEM 1. A miner is trapped in a mine containing 2 doors. The first doorleads to a tunnel that will take him to safety after 2 hours oftravel. The second door leads to a tunnel that will return him tothe mine after 3 hours travel. If the miner is at all times equallylikely to choose any one of two doors, what is the expected lengthof time until he reaches safety. PROBLEM 2. Consider $m$ independent flips of coins having probability$\frac{1}{3}$ of landing heads. A changeover occurs whenever anoutcome differs from the one preceding it. For instance, if $n=5$and the outcome is HHTHT, then there is a total of 3 changeovers. (a) Find the expected number of changeovers. (b) Determine the probability that there is exactly onechangeover. iLUSiON - le plus grand de tous http://cyworld.nate.com/ilusion |