Question

A committee 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?

Answer 1

Answer and explanation:

A = (4c2 / 10 * 1/10) + 4c3 / 10 = 0.46.

B) There is a 1/3 chance that the comittee will be tough and 2/3s that the comittee will not be tough.

This is because there's a 50% chance of approval and after an 80% chance of approval.

(1/3)∗(1/2)+(2/3)∗(4/5)=70