1. A multiple choice test has 12 questions with each question having 3 choices for its

answer. The test maker randomly numbers the three choices A, B, and C.

(a) What is the probability that the correct answer for all 12 questions is choice A (i.e., the

correct answers are A,A,A,A,A,A,A,A,A,A,A,A)?

(b) What is the probability that choice B is never the correct answer for the test?

(c) What is the probability that the correct test answers are (in the exact order):

A,B,C,A,B,C,A,B,C,A,B,C?

(d) If the test taker guesses randomly on each question, what is the probability that s/he will get

0% on this test?

2. For a computer system to function correctly, its three main components (HW, SW,

and user/operator) must each function correctly. The probability that each component works

correctly is:

Component / Probability that it works correctly

Hardware / 0.99999

Software / 0.9999

User/Operator (human) / 0.99

Assume that these 3 components work/fail (statistically) independently of each other.

(a) What is the probability that this computer system will work correctly?

(b) What is the probability that one or more of the computer system components will fail?

(c) Criticize our assumption that the hardware and software components fail independently of

each other.