Probability

Topics in this chapter

• Sample Spaces and Events
• Conditional and Bayes Probability
• Multiplication and Independence
• Random Variables and Moments
• Binomial Probability Models
• Card and Without-Replacement Probability

Cheat sheet

Practice questions

1. Question 1Q-1B81FE

   A bag contains 5 red balls and 3 blue balls. Two balls are drawn successively without replacement. What is the probability that the second ball is red, given that the first ball drawn is blue?

   1. A.5/8
   2. B.5/7
   3. C.3/7
   4. D.1/2
   See the answer and solution
2. Question 2Q-9D3D61

   The probability that a student has studied for a test is 0.6. The probability of answering a question correctly is 0.8 if the student has studied and 0.3 if the student has not studied. If the student answers correctly, what is the probability that the student had studied?

   1. A.0.6
   2. B.0.7
   3. C.0.8
   4. D.0.9
   See the answer and solution
3. Question 3Q-0C16EB

   A product is manufactured by machines M1, M2 and M3 in proportions 30%, 45% and 25%, respectively. Their respective defect rates are 2%, 3% and 5%. If a randomly selected product is found to be defective, what is the probability that it was manufactured by M3?

   1. A.25/64
   2. B.5/16
   3. C.25/32
   4. D.5/8
   See the answer and solution
4. Question 4Q-8DFD02

   If events A and B are independent, show that A and B' are independent and that A' and B' are also independent.

   See the answer and solution
5. Question 5Q-E40A2A

   A fair die is rolled once. What is the probability of getting an odd number, given that the number obtained is greater than 2?

   1. A.1/3
   2. B.1/2
   3. C.2/3
   4. D.1/6
   See the answer and solution