MODULE-1


1. Describe conditional probability with suitable examples.


2. Explain Normal distribution with suitable examples.


3. What is a random variable? Define expectation of random variables.


4. In how many different ways can 4 of 15 laboratory assistants be chosen to assist with an experiment?


5. If 5 of 20 tires in storage are defective and 5 of them are randomly chosen for inspection (that is, each tire has the same chance of being selected), what is the probability that the two of the defective tires will be included?


6. If 3 balls are “randomly drawn” from a bowl containing 6 white and 5 black balls. What is the probability that one of the balls is white and the other two black?


7. Assume that the probability that a wafer contains a large particle of contamination is 0.01 and that the wafers are independent; that is, the probability that a wafer contains a large particle is not dependent on the characteristics of any of the other wafers. If 15 wafers are analyzed, what is the probability that no large particles are found?


8. Explain the basic rules for probability.


9. An item is manufactured by three machines, M1, M2, M3. Out of the total manufacturing during specified production period, 50% are manufactured on M1, 30% on M2, and 20% on M3.it is also known that 2% of items produced by M1 and M2 are defective, While 3% of those manufactured on M3 are defective. All items are put into a bin. From the bin , One item is drawn random and found to be defective. What is the probability that it was made on M1, M2, M3???


10. A random variable X has a Poisson distribution with a mean of 3. Find P (1 ≤ X ≤ 3)?


11. Define following: 1) Random Variable; 2) Random Experiment; 3) Event


12. A committee of 5 is to be selected from a group of 6 men and 9 women. If the selection made randomly, what is the probability that the committee consists of 3 men and 2 women?


13. Five fair coins are flipped. If the outcomes are assumed independent, find the probability mass function of the number of heads obtained


14. If a fair coin is tossed twice, what is the probability of getting at least one head?


15. State Bayes Theorem. Suppose that a laboratory test to detect a certain disease has the following statistics. Let A = event that the tested person has the disease B = event that the test result is positive It is known that P(B / A) = 0.99 and P(B / A c ) = 0.005 and 0.1 percent of the population actually has the disease. What is the probability that a person has the disease given that the test result is positive?


16. Discuss various approaches to assign a probability in detail.


17. Differentiate between continuous and discrete random variables.


18. Explain Joint probability distribution with suitable example.


19. Define expectations of Random Variable and list its properties


20. In the inspection of tin plates produced by a continuous electrolytic process, 0.2 imperfections spotted per minute, on average. Find the probabilities of spotting 1. One imperfection in 3 minutes; 2. At least two imperfections in 5 minutes; At most one imperfection in 15 minutes.


21. Define variance of a Random Variable and list its properties


22. The probability that A hits a target is 0.25, and the probability that B hits the target is 0.4. Both shoot at the target. Find the probability that at least one of them hits the target


23. Three groups of children contain respectively 3 girls and 1 boy; 2 girls and 2 boys; 1 girl and 3 boys. One child is selected at random from each group, finding the probability that the selected group of three children consist of 1 girl and 2 boys.


24. Write a short note on 1) Sampling Distribution 2) Conditional Probability. 3) Mutually Exclusive Events 4) Random Variable.