1. We have two coins; the first is fair and the second two headed. We pick one of the coins at random,

we toss it twice and head shows both times. Find the probability that the coin picked is fair.

2. A lot of components contains 0.6% defectives. Each component is subjected to a test that correctly

identifies a defective, but about 2 in every 100 good components is also indicated defective. Given

that a randomly chosen component is declared defective by the tester, compute the probability

that it is actually defective.

3.Consider the following three events: (a) At least one six is obtained when six dice are rolled, (b) at

least 2 sixes are obtained when 12 dice are rolled, and (c) at least 3 sixes are obtained when 18

dice are rolled. Which of these events is more likely?

4.Consider the problem of computing reliability of so-called series-parallel systems. A series system

is one in which all components are so interrelated that the entire system will fail if any one of its

components fails. On the other hand, a parallel system is one that will fail only if all of its

components fail.

If a system consists of n components, and for i = 1, 2, ... , n, we define events Ai = "component i is

functioning properly." Let the reliability, Ri, of component i be defined as the probability that the

component is functioning properly; then Ri = P(Ai). Find the system reliability of:

a. The Series System (Hint: Use of intersection of the independent events Ais).

b. The Parallel System (Hint: First find the failure of the system by using intersection of

complements of the independent events Ais, as the parallel system fails if all n components

will fail. Finally, subtract the result from 1 to get the reliability).