Re: Daily question

Posted by Amit Goyal on Feb 17, 2009; 4:40pm
URL: http://discussion-forum.276.s1.nabble.com/Daily-question-tp2328964p2341832.html

Feb 17-20, 2009

In answering a question on a multiple choice test a student either knows the answer or he guesses. Let p be the probability that he knows the answer and 1-p the probability that he guesses. Assume that a student who guesses at the answer will be correct with probability 1/m, where m is the number of multiple choice alternatives. What is the conditional probability that a student knew the answer to a question given that he answered it correctly?

A miner is trapped in a mine containing three doors. The first door leads to a tunnel which takes him to safety after two hours' travel. The second door leads to a tunnel which returns him to the mine after three hours' travel. The third door leads to a tunnel which returns him to the mine after five hours' travel. Assuming that the miner is at all times equally likely to choose any one of the doors, what is the expected length of time until the miner reaches safety?

A family has two children. What is the conditional probability that both are boys given that at least one of them is a boy? Assume that the sample space S is given by S = {(b,b),(b,g),(g,b),(g,g)}, and all outcomes are equally likely. ((b,g) means for instance that the older child is a boy and the younger child a girl.)
Also find the conditional probability that both are boys given that at least one of them is a girl?

Two people share a room in a hospital.On any given day a person independently picks up an infection with probability 1/4.An individual who contracts its on a day will definitely pass it on to the other person (in the room) the next day.Once contracted the infection stays for two days.What is the probability that at the end of 2 days both patients have the infection?