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?