Acommittee of three judges is randomly selected from among ten judges. four of the ten judges are tough; the committee is tough if at least two of the judges on the committee are tough. a committee decides whether to approve petitions it receives. a tough committee approves 50% of petitions and a committee that is not tough approves 80% of petitions.

(a) find the probability a committee is tough.
(b) find the probability a petition is approved.
(c) suppose a petition can be submitted many times until it is approved. if a petition is approved with probability 3/4 each time, what is the mean number of times it has to be submitted until it is approved?

John, a 34 year old father of two children, is a member of a health maintenance organization (hmo) in texas. john has made several trips to an area clinic recommended by his hmo to seek medical attention since finding blood in his bowel movements. he has been taking large amounts of aspirin for persistent headaches but did not realize that this could cause internal bleeding. john was always seen at the clinic by a physician assistant, robert m. but never by a physician. robert didn't ask john about taking any nonprescription medications. john didn't realize that he should mention his over the counter medication (aspirin) consumption. robert tells john to take an antacid preparation to control the bleeding, but does not order any tests. he tells john to return if he is not any better. two days later, john is rushed to the area emergency room with a bowel hemorrhage.1-¿what responsibility, if any, does robert have for john's emergency? 2- does the clinic have a responsibility to provide its hmo members with the services of a physician? 3- what responsibility, as a healthcare consumer, does john have for his own medical condition?