CENTRO DE INVESTIGACIÓN Y
DESARROLLO DE EDUCACIÓN BILINGÜE
PROBABILITY AND STATISTICS – REVIEW I
Name: ______Id: ______
Group: ______Date: ______Score: ______
INSTRUCTIONS: Read carefully all the given information and write all the needed operations and steps. Otherwise your answer is NOT VALID.
1. Rewrite 7! with a factor of 5!
2. Represent 10! in the form n(n – 1)!
3. Rewrite 11! with the factor 8!
4. How many ways can 5 paintings be lined up on a wall?
5. In how many ways can 6 people line up at the ticket window?
6. Find the number of circular permutations of six people.
7. Find the number permutations of eight numbers on a spinner.
8. In how many ways can the 10 swimmers on an aquatic ballet team be arranged in a circular pattern?
9. In how many ways can letters of the set {R, S, T, U} be arranged to form ordered codes of 2 letters? (No letters are repeated.)
10. How many 5-digit numbers can be formed using all the digits 0, 1, 2, 3, 4 without repetition?
11. A woman is going out for the evening. She will put on one of 6 dresses, one pair out of 8 pairs of shoes, and go to one of 7 restaurants. In how many ways can this be done?
12. A fruit stand sells 9 different varieties of apples. How many different ways can the names of the apples be arranged on a sign?
13. In how many ways can 4 people be assigned to 6 one-person offices?
14. How many permutations are there of the letters in the set {M, N, O, P, Q, R, S}?
15. Find the number of permutations of the letters in DADDA.
16. Find the number of permutations of the letters of the word BANANAS.
17. Find the number of permutations of the letters in the word MISSISSIPPI.
18. Evaluate 5P5.
19. Evaluate 7P3.
20. How many combinations are there of the set {A, B, C, D} taken 3 at a time?
21. How many combinations are there of the set {A, B, C, D} taken 2 at a time?
22. For a sociological study 4 people are chosen at random from a group of 10 people. In how many ways can this be done?
23. How many ways can a congressional committee be formed from a set of 5 senators and 7 representatives if a committee contains 3 senators and 4 representatives?
24. In how many ways can a 5-player starting unit be selected from a 12-member basketball squad?
25. Simplify 9C5.
26. Evaluate 40C3.
27. Expand (r + s)6.
28. Expand (2a + 3b)4.
29. Find the 3rd term of the binomial expression (x – y)7
30. Find the 5th term of the binomial expression (w + 2z)8.
31. Determine the number of subsets of a set of 7 members.
32. Suppose we draw a card from a 52-card deck. What is the probability of drawing:
A) a heart? B) a Queen? C) an Ace or a Jack?
33. Suppose we select, without looking, one marble from a bag containing 4 red marbles and 10 green marbles. What is the probability of selecting:
A) a red marble? B) a green marble? C) a blue marble?
34. What is the probability of getting a total of 3 by rolling two number cubes?
35. What is the probability of getting a total of 7 by rolling two number cubes?
36. A card is drawn from a 52-card deck. What is the probability that the card will be:
A) a Spade or an Ace? B) a Heart or a Face Card?
37. A number cube is rolled twice. What is the probability of:
A) a 6 on the first roll and a 2 on the second roll?
B) a 3 on the first and second roll?
38. A number cube is rolled three times. What is the probability of rolling an:
A) even number on all three rolls?
B) odd number on the first roll, an even number on the second roll, and a prime number on the third roll?
39. Find the probability or each event. A card is drawn from a 52-card deck.
A) The card is a 7 or a King. B) The card is a Heart or a Diamond.
40. An urn contains 9 red, 4 blue and 5 black marbles. A marble is selected at random. Find each probability. A) The marble is red or blue. B) The marble is not red.
41. Find the probability of rolling a number cube and having a prime number or an even number show.
42. Find the probability, when drawing a single card from a standard 52-card deck, that the card is either a red or an Ace.
43. If P(A) = 0.37, P(B) = 0.55 and P(A Ç B) = 0.13. Find P(A È B)
44. If P(A) = 0.75, P(B) = 0.29 and P(A È B) = 0.88 and A and B are not mutually exclusive, find P(A Ç B).
45. If the probability it will snow on Monday is 25% and on Tuesday is 40%, what is the probability that it will snow on both Monday and Tuesday?
46. Find the probability of the toss of a coin landing heads up and the roll of a die showing a four.
47. An urn contains 4 red marbles and 3 green marbles. Find the probability of drawing a red marble, replacing it and then drawing a green marble?
48. Given that P(B) = 0.8 and P(A Ç B) = 0.6, find the P(A|B)
49. Given that P(C) = 2/3 and P(C Ç D) = 2/5, find the P(D|C)