Prob Questions

REVISIONARY QUESTIONS OF PROBABILITY FOR B. COM PART I 1. How many words can be formed from the letters of: i) HONEY ii) PASSENGER iii) NUMBER iv) DEPARTMENTALIZATION 2. Five lottery tickets are drawn from 20 for first five prizes. Find the number of elements in samples space. 3. How many 4 digit numbers can be formed using 0, 1, 3, 4, 7, and 9 without repetition. How many of the numbers formed are odd? 4. There are 3 books on Economics, 2 on Statistics & 4 on Accounting to be placed in a shelf. In how many ways can these books be arranged in the shelf if i) books on each subject are indistinguishable ii) all the three books on Economics should be placed with each other iii) the books on Statistics are to placed at the end. 5. In how many ways can 8 chairs be arranged in i) a line ii) a circle. 6. How many 6 letter words can be made from “format” if each letter can be used only once and i) there is no restriction ii) each word should start from t iii) each word should start from o and end with m 7. A car manufacturer offers 4 models of car, each with 7 choices of exterior color & 3 choices for interior color. How many choices does a customer have while purchasing a car? 8. From a group of 8 boys and 6 girls. In how many ways can 3 boys and 2 girls be selected? 9. From a group of 4 men & 5 women , how many committees of size 5 are possible if committee should contain: i) any person ii) 2 men & 3 women iii) 4 women iv) 3 men v) 5 men 10. Find the no. of ways in which 6 teachers can be assigned 4 classes i) if no teacher is assigned more than 1 class ii) if a teacher can be assigned more than 1 class 11. 7 cards are drawn from a deck of 52 playing cards. How many groups of these 7 cards would contain i) 5 black and 2 red cards ii) 3 aces iii) 4 face cards iv) 2 diamonds & 3 hearts 12. Two pairs of fair coins are tossed at a time. What is the probability of getting: i) 2 heads ii) 3 tails iii) at most 2 heads iv) at least 3 tails. 13. A pair of dice is rolled once. What is the probability of getting: i) same no. on both dice ii) sum of digits greater than 9 iii) product of no. greater than 12. 14. The summary of unit sold of product A in previous months is as follows: No. of units sold No. of months On the basis of past records, what is the probability that no. of units sold in the next month be 6000-8000 22 i) more than 12000 ii) less than 10000 8001-10000 45 iii) between 6000 to 10000 iv) more than 8000 10001-12000 32 More than 12000 21

15. If P(A)=0.4 ,P(B)=0.55 & and both are independent events, then find P(AnB), P(AnB), P(AuB), P(AnA), P(AnB). 16. If P(A)=0.7, P(B)=0.25 & P(AuB)=0.95 then find P(AnB) 17. If P(A)=0.2, P(B)=0.65 & P(AnB)=0.15 then find P(A|B), P(B|A). 18. If probability that Mr. A & Mr. B will be alive after 40 years is 0.45 & 0.65 respectively, then what is the probability that after 40 years i) both will be alive ii) at least one will be alive iii) only A will be alive iv) both will be dead. 19. In a town 25% families own car, 40% families have motorcycles and 15% families have both vehicles. If a family is chosen from this town then what is the probability that it has i) at least one vehicle ii) a car given that it has a motorcycle iii) a motorcycle given that it has a car. 20. A multiple choice test contains 12 questions, each with 4 choices of which only one is correct. If a student guessed all the question then what is the probability that he will guess i) 7 questions correct ii) 6 questions wrong iii) at least 9 questions correct iv) at most 10 questions correct. What is the expected no. of the correct answers in the test? 21. On a biased coin head appears 70% of the time tossed. If this coin is tossed 20 times then what is the probability of getting: i) 10 tails ii) at least 17 heads. What is the expected no. of the tails in this experiment? 22. No. of phone calls on my cell phone follows a Poisson distribution with a mean of 6 calls in a day. What is the probability that no one will call me in 2 days? What is the maximum no. of calls that can be received in a day? 23. The average no. of accidents on a particular traffic signal is 2 per week. If a 3 week period is observed then what is the probability of occurrence of: i) no accident ii) at most 2 accidents iii) at least 2 accidents. What is the standard deviation in no. of accidents? 24. From a deck of 52 playing cards, six cards are selected at random. What is the probability that of getting: i) 4 kings ii) 3 red cards iii) 2 spades & 3 hearts iv) 4 numbered cards v) 5 spades or 3 diamonds vi) 3 numbered cards or 2 face cards 25. A bag contains 4 red, 6 white & 7 green balls. If 4 balls are selected at random then what is the probability of getting: i) 4 white balls ii) 1 red, 3 green balls iii) no white ball iv) at least 2 green balls. 26. The average life of Exide batteries is 60 weeks with a standard deviation of 12 weeks. If you purchase an Exide battery then what is the probability that it will last i) less than 75 weeks ii) at least 30 weeks iii) more than 40 weeks but less than 80 weeks.

27. Average wages of workers in a factory is Rs. 300 per day with a variance of Rs. 900. If a worker is selected at random, then what is the probability that he will be earning i) at least 330 per day ii) between 250 to 380. What will be the lowest pay among the most highly paid 20% workers? What is the highest pay among the most lowly paid 40% workers? 28. In a game, a person will win Rs. 10 if head appears on a biased coin having 40% chances of head and lose Rs. 8 if tails appears on the coin. What is the expected gain/loss in this game?