Class work 1

1. Class work 1 • Two fair dice are thrown at random. What is the probability that the turn up show • a sum 7 • sum of 8 or 9 • a sum less than 5 • the two dice show the same number • the product of the two number is even.

2. Class work 2 • A bag contains 30 balls numbered from 1 to 30. If one ball is drawn at random from the bag, what is the probability that drawn ball is • Multiple of 3 • multiple of 5 • multiple of 3 and 5 • multiple of 3 or 5 • even number

3. Class work • The HAL corporation wishes to improve the resistance of its personal computer to disk driver and key board failures. At present , the design of computer is such that disk-drive failures occur only one third as often as keyboard failures. The probability of simultaneous disk-drive failures is 0.05. • If the computer is 80% resistant to disk-drive and/or keyboard failure, How low must the disk-drive failure

4. Continue • If the keyboard is improved so that it fails only twice as often as the disk-drive( and the simultaneous failure probability is still 0.05), Will the disk drive failure probability from part (a) yield a resistance to disk-drive and /or keyboard failure higher or lower than 90%.

5. Class work 3 • A stockiest has 20 items in a lot; out of which 12 are non defective and 8 defective. A customer selects 3 items from the lot. What is the probability that • All the three are non defective • Two are non defective and one is defective

6. Class work 4 • Five men in a company of 20 are graduates. If 3 men are picked out of the 20 at random, what is the probability that they are • all graduates • all non-graduates • 2 graduates • at most 1 graduates • at least one graduates • 2 non graduates

7. Class work • A box contains 5 red and 4 blue balls .Two balls are drawn at random from the box.Find the probability that both of them are red: • If balls are drawn together • Balls are drawn one after another, with replacement • The balls are drawn one after another, without replacement

8. Class work 5 • A sample of 500 respondents was selected in a large metropolitan area in order to determine various information concerning consumer behavior. Among the question asked was” do you enjoy shopping for clothing?" Of 240 males, 136 answered yes. Of 260 females, 224 answered yes. • Set up the 2X2 table • What is the probability that a respondent chosen at random • is a male? • enjoys shopping for clothing? • is females? • is females and enjoys shopping for clothing? • is male and does not enjoys shopping for clothing? • is females or enjoys shopping for clothing? • is male or females? • Suppose the respondent chosen is a female. What then is the probability that she does not enjoy shopping for clothing? • Suppose the respondent chosen enjoys shopping for clothing. What then is the probability that the individual is a male?

9. Class work 6 • Given that P(A) = 3/14, P(B) = 1/6, P(C) = 1/3 ,P(AC) = 1/7 and P(B/C) = 5/21. Find the following probabilities: • P(A/C) • P(C/A) • P(BC) • P(C/B)

10. Class work 7 • During a study of auto accidents, the Highway Safety Council found that 60 percent of all accidents occur at night, 52 percent are alcohol related and 37 percent occur at night and are alcohol related. • What is the probability that an accident was alcohol related given that it occurred at night? • What is the probability that an accident occurred at night given that it was alcohol related?

11. Class work 8 • The southeast regional manager of General Express, a private parcel delivery firm is worried about the likelihood of strikes by some of his employees. He has learned that the probability of a strike by his pilots is 0.75 and the probability of a strike by his drivers is 0.65. Further, he knows that if the drivers strike, there is a 90 percent chance that the pilots will strike in sympathy. • What is the probability of both groups striking? (0.585) • If the pilots strike, what is the probability that the drivers will strike in sympathy? (0.78)

12. Class work 9 • According to a survey of American households, the probability that the residents own 2 cars if annual household income is over $25,000 is 80% .of the households surveyed, 60% had incomes over $25,000 and 70% had 2 cars. • What is the probability that the resident of a household do not own 2 cars and have an income over $25,000? • What is the probability that annual household income is over $25,000 if the residents of a household own 2 cars? • What is the probability that the residents of a household own 2 cars and have and income less than or equal to $ 25,000 a year?

13. Class work 10 • The chance a customer will order a bottle of coke in a fast food restaurant is 0.9. The probability that a customer will order a hamburger is 0.6. The probability that a customer will order French fries is 0.50. You are required to answer the following questions in this regard. • If customer places an order ,what is probability that the order will include coke and no French fries if these two events are independent

14. Continue………. • If a customer places an order, what is the probability that the order will include coke and Hamburger if these two events are independent • The manager has also determines that if a customer orders hamburger, the probability that the customer will also order French fries is 0.8. Further he has noticed that if a customer orders French fries, the probability that will also order coke is 0.95

15. Continue…….. • Determine the probability that the order will include hamburger and French fries. • If a customer orders French fries, what is probability that the customer will also order hamburger? • If a customer orders a bottle of coke, what is the probability that the customer will order French fries