1. Three cards are drawn from a 52 card deck - no replacement. What is the probability that the last two draws are aces if the first was an ace?

2. A certain telephone number has 7 digits. If the telephone number as the digit 0 exactly three times, and the number one is not used at all, what is the probability that the phone number contains 1 or more prime digits?

3. N is from 1 to 96, what is the probability of N such that N(N+1)(N+2)is evenly divisible by 8?

4. In how many ways 30 couples(total=30 men and 30 women...with respective man sitting on the right of woman) and 30 HOD(head of the department) be seated around a round table if each of the couple should sit between each of the HOD?

5. In the United States, 43% of people wear a seat belt while driving. If two people are chosen at random, what is the probability that both of them wear a seat belt?

6. Find the number of m seven-letter words that can be formed using the letters of the word BENZENE.

7. In how many ways can 6 people be seated in a circle if 2 people are always separated?

8. In a bag of balloons, the ratio of red balloons to other is 1:5if 3 Bal. are selected at random, what is the prob that -

1. At least one bal is red (I can get both - 91/216 and 31/216 as answers without any doubts but one is wrong. I dont know why.)

2. exactly one bal.is red.

9. Two girls have their birthdays in the same week.It is known that one of the girls was born on a saturday. determine the prob that both were born on a saturday.

10. There are Two groups.

Grp A has : 7Boys 3 girlsGrp B has : 3Boys and 8Girls

If two persons are selected from either of the grps A or B, find the Prob. thata. Both are boysb. one is a Boy, one is Girl

11. In how many ways could the letters in the word MINIMUMbe arranged if the U must not come before the I's?

12. Two canoe riders must be selected from each of two groups ofcampers. One group consists of three men and one woman, andthe other group consists of two women and one man. What isthe probability that two men and two women will be selected?

a. 1/6 b. 1/4 c. 2/7 d. 1/3 e. ½

13. What is the probability that in a group of 10 studentsat least 2 will have the same birthday?

14. When 2 friends, Ram and Gopal, play carrom, Ram wins60% of the time and Gopal 40% of the time. However,Ram will win 2 in a row 50% of the time. If it isgiven that Ram has won the 1st game of a match, whatis the probability that he wins the second?

15. 10 slips of paper, each containing the name of adifferent child, were placed into a hat. 2 slips weredrawn at random and the names recorded in that order.What is the probability that Barb's and Alice's namesare drawn in that order?

16. Given letters ABCCD how many different ways can a group of 3 can be formed with these letters.

17. For a set of numbers composed of positive integers ranging from 1-99 (inclusive),we take a number N from the set, what is the probability of n*(n+1) that can be divisible by 3?

18. 3 representative from 6 companies. shake hands only with other companies' representative. representative from same company does not shake hanks. Total how many hand shakes?

19. 2 bunch of redrose, 2 bunch of white rose, What is the probability of planting them in a row with two red in the middle.

20. A couple has 4 children, What is the probability of 2 boys, 2 girls?

21. 200 person have pager, cell phone or both. 160 have cell phones, 90 have pagers. How many person either no cell phone or no pager?

22. A's breakfast has 2 chiken sandwish and 4 cheese sandwish;B's breakfast has 3 chiken sadwish and 5 cheese sandwish. Choosing 1 from each meal randomly, what is the probability of both are chicken?

23. In an insurance company, each policy has a paper record and an electric record. For those policies having incorrect paper record,

60% also having incorrect electric record; For those policies having incorrect electric record, 75% also having incorrect paper record. 3% of all policies have both incorrect paper and incorrect electric records. If we randomly pick out one policy, what's the

probability that the one having both correct paper and correct electric records?

24. A is given a phone list containing 200 different phone numbers B is given the same phone list A and B are ask to call one phone number at the same time. What is the probability that A and B call the same number?

25. S set = (-6,-5,-3,-2,-1) T = (-2,-1,0,1,2,3) One number is selected from S, and the other number is selected from T. What is the probability that the product of the two number is negative?

26. You are given a deck of 52 cards. The cards are numbered from 1 to

52. The deck is shuffled thoroughly. Five cards are picked randomly (without replacement) from the deck. What is the probability that the five cards will be picked in ascending order (for example, the card labeled "3" is picked first, followed by the one labeled "9", followed by the "22", followed by the "48", followed by the "50")?

27. A and B are highly truthful (they each tell the truth randomly 3/4 of the time. Also, A's and B's truthfulness are independent. Suppose A and B both look out the window to see what the weather is like. A says, "It's raining." B says, "It's raining." What is the probability that it actually is raining.

28. Grp A: 7Boys 3 girlsGrp B: 3B and 8G

If two persons are selected from either of the grpsAor B, find the Prob. thata. Both are boysb. one is B, one is G

29. One poorly worded Question:There are two lines of defence against an attackingaircraft. 1st id missile and 2nd is anti-aircraft gun.the respective prob. that the aircraft being hit bythe missile and the gun are 2/9 and 1/8 respcly. what is the prob. of hitting the aircraft?

30. In a raffle in which 200 tickets are sold,there are 3 prizes - first prize of $100, second prizeof $50, third prize of $30.

(i) A man has 2 tickets in this raffle. WHat is theprobability that he wins (a) a prize, (b) both prizes.

31. (i) From an ordinary deck of cards, only 12 picturecards are retained. They are shuffled (mixed) and aman draws 2 cards at random. He then announce one ofthese cards is the King or Spades. What is theprobability that he holds two Kings? (hint: list thepossible sample space carefully).

(ii) The 2 cards are replaced and the cardsre-shuffled. He then draws 2 cards, and announces thathe holds at least one King. Find the probability thathe holds two Kings in his hand.

32. A girl has 5 pairs of shoes. each pair being a diff style.If she selects 2 shoes at random, what is the Prob. they form a maching pair?

33. In a college housing lottery, 1 out of every 5 applicants is offered college housing. If a student is entered in the lottery, two years in a row. What is the probability the student is offered the housing?

34. A fair coin is tossed 5 times. What is the probability of throwing

at least two heads?

35. In how many ways can 3 girls and 9 boys be seated in 2 vans each having numbered seats, 3 seats in the front and 4 at the back?b) How many seating arrangements are possible if 3 girls should sit together in the back seats adjacent to each other. c) If all seating arrangements are equally likely what is the probability of 3 girls sitting together in a back row on adjacent seats.

36. A bag contains 10 white and 3 Black balls while another bag contains 3 white and 5 black balls. Two balls are drawn at random from the first bag and then put into the second bag. Now a ball is

drawn at random from the second bag. find the probability of getting a white ball?

a) 15/52b) 10/36c) 3/260d) 59/130e) 13/21

37. A man is known to speak the truth 3 out of 4 times. He throws a dice and reports that it is 6. The probability that it is actually

rigt is

a) 3/8b) 1/5c) 3/5d) 1/3e) 5/8

38. Three of the six vertices of a regular hexagon are chosen at random. What is the probability that the triangle drawn with these

three vertices is equilateral.

a) 1/2b) 1/5c) 1/10 d) 1/20e) 3/20

39. chances of heads coming in tossing a coin is ½. what is the prob of heads coming at least once in 3 tosses?

40. 4 boxes have each M # of marbles, how many should be removed from the first to the remaining 3 to make the ratio 1:6:3:4

41. A box has 16 cubes, 5 red, 3 green and rest yellow. If four cubes are picked without replacement, then what is the probability that "at least three" are red?

42. In a drawer of shirts, 8 are blue, 6 are green and 4 are magenta. If Mason draws two shirts at random, what is the probability at least two of the shirts he draws will be blue?

43. What is the probability that the product of any 2 of these expression (x+y), (x-y), (x-5y), (5x+y) be of the form (x-(by)^2)?

44. Medical researchers know that the probability of getting lung cancer if a person smokes is .34. The probability that a nonsmoker will get lung cancer is .03. It is also known that 11% of the population smokes. What is the probability that a person with lung cancer will have been a smoker?

45. If 3 of 20 Firestone tires are defective and 4 of them are randomly chosen for inspection, what is the probability that only 1 of the defective tires will be included?

46. There are 5 English, 3 Spanish and 2 Portuguese books on a shelf. If 2 books are selected without replacement what is the probability that theywill be of different languages.

47. There are 5 English, 3 Spanish and 2 Portuguese books on a shelf. If 2 books are selected without replacement what is the probability that they will be of different languages.

48. There are 1200 students in a class. All have taken maths or science or both. If 300 students have taken only english and 500 have only maths, how many have taken both.

49. A large cube 10cm on a side is composed of smaller cubes 1 cm on a

side. The large cube is printed red on its outside surfaces and then all the cubes are mixed in a drum. If one cube is selected randomly, which of the following is the approximate probability that the cube will have at least one red face?

A) 1:6

B) 1:5

C) 1:4

D) 1:3

E) 1:2

50. Find the probability that a number from the set {1,2,3 ......1001}is divisible by 7 or 11 (or both).

51. Bob sells one design of Ferrari cars. One type has 10 cylinders,and the other type has 12 cylinder. Both of these come in eitherstick-shift or automatic. You can get extra-wide tires, butonly with the 12-cylinder Ferrari. How many different types ofthis Ferrari does Bob sell?

52. What is the probability that events A and B both occur?

1) The probability that event A occurs is 0.82) The probability that event B occurs is 0.6

53. There are 8 yellow balls and 5 green balls in a bowl. If you reach in the bowl 3 times and grab one ball each time, what are the chances that you will have 2 yellow balls and 1 green ball?

54. –2/22/0255.