Prof. L. Shridharan

PRACTICE PROBLEMS

1.(a) What is the probability that a leap year selected at random will contain 53 Tuesdays? (b)What is the probability that a leap year selected at random will contain 53 Sundays or 53 Mondays?

2.A bag contains 8 black, 3 red and 9 white balls. If 3 balls are drawn at random , find the probability that (a) all are black, (b) 2 are black and 1 is white, (c) 1 of each colour, (d) the balls are drawn in the order black, red and white, (e) None is red.

3.From a pack of 52 cards, 4 are accidentally dropped. Find the chance that (a)they will consist of a jack, a queen, a king and an ace. (b)They are from the same suit.

(c)They are one from each suit.

(d)Two of them are red and two are black.

4.A six figure number is formed by the digits 4, 5, 6, 7, 8 & 9 ; no digit being repeated. Find the chance that the number formed is : (a) divisible by 5. (b) not divisible by 5.

5.The probability that a contractor will get a plumbing contract is 2/3, and the probability that he will get an electric contract is 5/9. If the probability of getting at least one contract is 4/5, what is the probability that he will get both the contracts?

6.The probability that a management trainee will remain with a company is 0.6. The probability that an employee earns more than Rs.10,000 per month is 0.5. The probability that an employee is management trainee who remained with the company or who earns more than Rs.10,000 per month is 0.7. What is the probability that an employee earns more than Rs.10,000 per month, given that he is a management trainee who stayed with the company?

7.A piece of electronic equipment has two essential parts A and B. In the past, part A failed 30% of the times, part B failed 20% of the times and both failed simultaneously 5% of the times. Assuming that both parts must operate to enable the equipment to function, what is the probability that the equipment will function?

8.A salesman has a 60% chance of making a sale to each customer. The behaviour of successive customers is independent. If two customers A and B enter the shop, what is the probability that the salesman will make a sale to A or B?

9.Suppose that a product is produced in 3 factories A, B & C. It is known that A produces twice as many items as B, and that B & C produce the same number of items. Assume that it is known that 2% of items produced by each of A & B are defective, while 4% of those of C are defective. All items produced in three factories are stocked, and an item is selected randomly. What is the probability of this item being defective?

10.In a population of workers, 40% are primary school graduates, 50% are high school graduates and 10% are college graduates. The unemployment rates among the 3 categories are respectively 10%, 5% & 2%. If a worker is chosen at random and found to be unemployed, what is the probability that he is a college graduate?

11.Air Corporation, having had just 2 air-crashes during its first fifty years of existence, wants to make the next decade “air-crash free”. Assuming that the same trend will continue, what is the probability of the Corporation meeting the target?

12.A distributor of bean seeds determines from extensive tests that 5% of large batch of seeds will not germinate. He sells the seeds in packets of 200 and guarantees 90% germination. Determine the probability that a particular packet will violate the guarantee.

13.The life time in hours of certain electrical equipment has the normal distribution with mean at 80 hours and standard deviation at 16 hours. (a)What is the probability that the equipment lasts at least 100 hrs.? (b)If the equipment has already lasted 85 hours, what is the conditional probability that it will last another 15 hours?

14.A sample of 100 dry battery cells, tested to...