Probability - Scarsdale Public Schools



1) A pair of six-sided dice is rolled, and the sum is recorded. What is the probability that this sum is a multiple of three? (2) 2004-WU4-7

2) Michael spins the spinner twice. All three of the larger sectors are equal in area and have central angles of 90º. The two smaller sectors have equal area. What is the probability that he will “WIN” on both spins? (3) 2004-WU5-4

Win Lose

Lose

Lose Lose

3) In a school of 250 students, everyone takes one English class and one History class each year. Today, 15 total students were absent from their English class and 10 total students were absent from their History class. Five of the students were absent form both classes. If a student is chosen at random from this school, what is the probability that s/he was not absent from either class? (2) 2004-WU7-6

4) Rodney uses the following clues to try to guess a secret number:

It is a two-digit number.

The tens digit is odd.

The units digit is even.

The number is greater than 65.

If Rodney guesses a number that has each of these properties, what is the probability that Rodney will guess the correct number? (1) 2004-WU8-1

5) John, Kevin, Larry, Mary and Nancy all volunteered to so some math tutoring. If their teacher randomly chooses two of the five students, what is the probability of selecting the two girls? (3) 2004-WU8-9

6) A magician designed an unfair coin so that the probability of getting a head on a flip is 60%. If he flips the coin three times, what is the probability that he flips more heads than tails? (3) 2004-WU12-8

7) Sal has three quarters, three nickels and three pennies. If Sal selects three coins at random and without replacement, what is the probability that he total value is exactly 35 cents? (3) 2004-WO6-10

8) Ann rolls a die twice. What is the probability of getting numbers with a positive difference of 1? (3) 2004-WU13-9

9) Sue owns 11 pairs of shoes: six identical black pairs, three identical brown pairs and two identical gray pairs. If she picks two shoes at random, what is the probability that they are the same color and that one is a left shoe and the other is a right shoe? (3) 2004-WU14-9

10) A box contains two coins with a head on both sides, one standard coin and one coin with a tail on both sides. A coin will be randomly selected from these four coins and will be flipped twice. What is the probability that each of the two flips will result in a head? (3) 2004-WU15-8

11) A box contains six cards. Three of the cards are black on both sides, one card is black on one side and red on the other, and two of the cards are red on both sides. If you pick card at random from the box and see that the side facing you is red, what is the probability that the other side is red? (3) 2004-WO8-10

12) Marty has one standard quarter and one special quarter with a head on both sides. He selects one of these two coins at random, and without looking at it first, he flips the coin three times. If he flips a head three straight times, what is the probability that he selected the special quarter? (3) 2004-WU18-10

13) A bowl contains 10 jellybeans (four red, one blue and five white). If you pick three jellybeans from the bowl at random and without replacement, what is the probability that exactly two will be red? (3) 2004-WO9-10

14) Manny and Jami are playing a coin toss game with a fair penny. Manny gets a point if the penny lands on heads, and Jami gets a points if the penny lands on tails. The score is Jami 9, Manny 7, in a game to 10 points. What is the probability that Jami will win the game? (2) 1999-WU1-4

15) A bag contains one marble, either green or yellow. A yellow marble is added to the bag, and one marble is randomly chosen. The chosen marble is yellow. What is the probability that the marble left in the bag is yellow? (3) 1999-WU15-1

16) A best of five series ends when one team wins three games. The probability of team A defeating team B in any game is [pic]. What is the probability that team A will win the series? (3) 1999-WO7-1

17) If two distinct numbers are selected at random from the first seven prime numbers, what is the probability that their sum is an even number? 2000-WU6-7 (2)

18) A bag contains 7 white, 9 blue and 4 red marbles. If three marbles are pulled from the bag, what is the probability that two are blue and one is red? 2000-WU6-4 (3)

19) A circuit contains two switches. The first switch transmits a message correctly 80% of the time, and the second switch transmits a message correctly 90% of the time. What percent of the time will the message be transmitted successfully through both switches? 2000-WU10-3 (1)

20) Four prime numbers are randomly selected without replacement from the first ten prime numbers. What is the probability that the sum of the four selected numbers is odd? 2000-WU10-6 (1)

21) Flip a fair coin. If it lands heads, write H and the turn is done. If it lands tails, then flip it again – write H if it lands heads or T if it lands tails, and the turn is done. After five turns, what is the probability that 5 H’s have been written? 2000-WU14-5 (3)

22) Two standard dice are rolled. What is the probability that the product of the two numbers rolled exceeds 8? 2000-WO1-3 (2)

23) Chuck is going on a four-day vacation. The probability for a rain is 40% on Friday, 30% on Saturday, 60% on Sunday, and 50% on Monday. What is the probability that Chuck has a rain-free weekend? Express as a decimal to the nearest thousandth.2000-WO3-1 (2)

24) David randomly selected three different integers 1 through 6. What is the probability that the three numbers selected could be the sides of a triangle? 2000-WO5-3 (2)

25) At a random time during her 45-minute class, Mrs. Ritter gives a 5-minute pop quiz. If your are nine minutes late for class one day, what is the probability you missed the start of the quiz? 2003-WU12-8 (2)

26) A scratch off lottery ticket has six spaces that can be uncovered. Two of the six spaces are WIN; the other four are LOSE. A player randomly uncovers two spaces. If she gets both WIN spaces, she wins a large prize. If she uncovers one WIN and one LOSE she gets a small prize. What is the probability that she gets a small prize? 2003-WO7-9 (3)

27) There are 5 blue chips and 3 yellow chips in a bag. One chip is drawn from the bag. That chip is placed back into the bag. A second chip is then drawn. What is the probability that the two selected chips are of different colors? 2003-WU15-9 (3)

28) A number is randomly selected from the set of consecutive integers

{1, 2, 3, … ,720}. What is the probability that the number is a factor of 6!?

2003-WO8-3 (3)

29) Amy was born on a Tuesday. What is the probability that exactly two of her three best friends were also born on Tuesday? 2003-WU17-6 (3)

30) The probability of snow for each of the next three days is ¾. What is the probability that it will not snow any of those days? 2003-WU18-6 (2)

31) A drawer contains five red socks and eight blue socks. Leo reaches into the bag and randomly selects two socks without replacement. What is the probability that Leo will get different-colored socks? 2003-WO9-2 (3)

32) Two different natural numbers are selected from the set {1, 2, 3, . . ., 6}. What is the probability that they are relatively prime? (2) 2002-WU1-1

33) Three standard dice are tossed. What is the probability that the sum of the three numbers tossed is 17 or greater? (2) 2002-WU3-10

34) Chris sleeps from 10:30 p.m. to 6:30 a.m. At a random time during the night, he awakens and looks at his clock. What is the probability that it is before midnight? (2) 2002-WU5-2

35) The digits from 1 to 6 are arranged to form a six-digit multiple of 5. What is the probability that the number is greater than 500,000? (2) 2002-WU5-8

36) Three segments are chosen at random from six segments having lengths of 2, 3, 5, 6, 7 and 10 units. What is the probability that the three segments chosen could form a triangle? (2) 2002-WU10-3

37) A fair six-sided die is rolled. Statement P is true if the die reads 1 or 2. Otherwise P is false. Statement Q is true if the die reads an even number. Otherwise Q is false. What is the probability that statement P or Q is true? (2) 2002-WU10-3

38) A bag contains 12 red marbles and 6 blue marbles. Two marbles are selected at random and without replacement. What is the probability that one marble is red and one is blue? (3) 2002-WU12-7

39) Two different numbers are selected at random from the set {1, 2, 3, 4, 5, 6, 7}. What is the probability that the positive difference between the numbers is 2 or greater? (2) 2002-WU14-7

40) Bob and Megan play a two-person game which is won by the first person to accumulate 10 points. At each turn Bob gains a point with probability of 1/3. If he doesn’t get a point, then Megan gets a point. Megan is now ahead 9 to 8. What is the probability that Megan will win? (2) 2002-WU14-10

41) In a video game, each rocket has an 80% chance of hitting a target. Three rockets are now fired at a target. What is the probability that exactly two of the rockets will hit the target? Express as a decimal to the nearest thousandth. (3) 2002-WO7-4

42) Two standard six-sided dice are rolled. Cara scores x points if the sum of the numbers rolled is greater than or equal to its product, otherwise Jeremy scores 1 point. What would be the value of x to make the game fair? (3) 2002-WO8-8

43) Given that you randomly guess the answers to ten true-false questions, determine the probability that you get all ten correct? (3) 1997-WU5-5

44) If one letter is randomly selected from the word MATH and one letter is randomly selected from the word COUNTS, what is the probability that at least one of the letters is a vowel? (3) 1997-WU6-5

45) Chen’s math teacher gives homework four out of every five school days. Her science teacher gives homework three out of every four school days. What is the probability that on a particular school day Chen does not have homework in either subject? (2) 1997-WU11-1

46) Ronnie, Ben and Jevon are in the same math class. There are 24 students in the class, and the teacher has announced that she will be dividing the class into groups of 3. What is the probability that Ronnie, Ben and Jevon will be in the same group? (3) 1997-WU14-4

47) In Mike’s piggy bank, there are twice as many dimes as quarters, five times as many nickels as quarters, and twice as many pennies as all other coins combined. It is equally likely that any one of the coins will fall out when the piggy bank is turned upside-down. Calculate the probability that either a nickel or a quarter will fall out. (2) 1997-WU16-3

48) The exercise room at work is open Monday through Friday for use by employees. Jane exercises two days each week, and Richard exercises two days each week. They independently decide which two days every week. What is the probability that they will be there on the same day at least once in a given week? (3) 1997-WU18-1

49) Given that a and b are integers such that (3 ( a ( 1 and (1 ( b ( 3, and values for a and b are chosen at random, what is the probability that ab is not negative? (3) 1997-WO1-2

50) What is the probability that the sum of the numbers on two randomly tossed standard dice is greater than 7? (2) 1997-WO3-3

51) There is a 50% chance of rain on Saturday. If there’s rain on Saturday, then there is a 60% chance of rain on Sunday. If there’s no rain on Saturday, then there’s a 40% chance of rain on Sunday. What is the probability of two days without rain this weekend? (3) 1997-WO8-3

52) Rick has 6 different pairs of socks. What is the probability that two randomly selected socks will be from a matching pair? (3) 2001-WU1-6

53) In a bag, there are 3 red marbles and B blue marbles. Two marbles are randomly selected from the bag without replacement. The probability that the two marbles are the same color is 0.5. Calculate the sum of all possible values of B. (3) 2001-WU2-10

54) Aimee tosses one fair 6-sided die labeled 1 through 6 and one fair 4-sided die labeled 1 through 4. What is the probability that the sum Aimee rolls is less than 5? (2) 2001-WU5-6

55) On a trick 6-sided die the probability of rolling a 1 or 2 is each 1/4, the probability of rolling a 3 or 4 is each 1/6 and the probability of rolling a 5 or 6 is each 1/12. The trick die and a standard die are rolled. What is the probability of rolling a sum of 7? (3) 2001-WU7-9

56) Becky has 10 brown socks and 10 black socks. If she randomly selects two socks from the drawer simultaneously, what is the probability that they are the same color? (3) 2001-WU10-5

57) Two standard 6-sided dice are tossed. What is the probability that the sum of the two numbers rolled is greater than nine? (2) 2001-WU13-7

58) A store offers customers a game car with 5 scratch-off circles, each hiding a percent discount: 50%, 50%, 25%, 10%, 5%. The customer selects two circles to uncover and receives a discount equal to the average of the two values. What is the probability of receiving a 50% discount? (2) 2001-WU15-7

59) Each of four cards has a different numeral written on one side of it. The same four numerals are written on the other side of the cards in a random order, one on each card. What is the probability that at least one of the cards will have the same numeral written on both sides? (3) 1996-WU17-5

60) You have a penny, a nickel and two dimes in your pocket. You take out two coins, one after the other. What is the probability that the value of the first coin is smaller than the value of the second? (3) 1996-WO8-5

61) You have two quarters, three dimes and four nickels in your pocket. You reach into your pocket and randomly select three coins. What is the probability that their value is exactly 25 cents? (3) 1996-WO8-9

62) Given that the numerator of a fraction is randomly selected from the set

{1, 3, 5, 7, 9} and the denominator is randomly selected from the set {1, 2, 3, 4, 5}, what is the probability that the decimal representation of the fraction is a terminating decimal? (3) 1996-WO9-9

63) There are six sticks with respective lengths of 3, 4, 5, 6, 8 and 10 units. Three of these sticks are chosen at random. What is the probability that the three sticks chosen can form a triangle? Express as a decimal to the nearest hundredth. (3) 2001-WO10-6

64) The faces on a regular octahedral die are numbered one through eight. What is the probability of rolling 3 sixes in succession? (2) 1993-WU10-5

65) Two standard dice are thrown. What is the probability that a prime sum is rolled? (2) 2001-WO2-4

66) If a five-question True/False test is given and 60% is a passing grade, what is the probability, to the nearest whole percent, of passing if you guess on each question? (3) 2001-WO3-3

67) If a ten-question True/False test is given and 60% is a passing grade, what is the probability, to the nearest whole percent, of passing if you guess on each question? (3) 2001-WO3-4

68) In Ms. Smith’s class, each student averages one day absent out of thirty. What is the probability that out of any two students chosen at random, one student will be absent while the other is present? Express as a percent to the nearest tenth. (3) 2001-WO4-10

69) a is randomly selected from the set {2, 3, 4, 5}, replaced, and then b is randomly selected from the same set. What is the probability that the fraction [pic] is already in reduced form? (3) 1993-WO10-3

70) Deb has a 1/5 chance of hitting a bull’s-eye with one dart. If she tosses 5 darts, what is the probability that she will hit at least one bull’s-eye. Express as a decimal. (3) 1993-WO7-9

Probability - Answer Key

1) 1/3

2) 1/64

3) 92%

4) 1/10

5) 1/10

6) 81/125

7) 3/28

8) 5/18

9) 7/33

10) 9/16

11) 4/5

12) 8/9

13) 3/10

14) 7/8

15) 2/3

16) [pic]

17) 5/7

18) 12/95

19) 72%

20) 2/5

21) 243/1,024

22) 5/9

23) .084

24) 7/20

25) 9/40

26) 8/15

27) 15/32

28) 1/24

29) 18/343

30) 1/64

31) 20/39

32) 11/15

33) 1/54

34) 3/16

35) 1/5

36) 9/20

37) 2/3

38) 8/17

39) 5/7

40) 8/9

41) .384

42) 2

43) 1/1,024

44) 1/2

45) 1/20

46) 1/253

47) 1/4

48) 7/10

49) 3/5

50) 5/12

51) 3/10

52) 1/11

53) 7

54) 1/4

55) 1/6

56) 9/19

57) 1/6

58) 1/10

59) 5/8

60) 5/12

61) 1/7

62) 22/25

63) .65

64) 1/512

65) 5/12

66) 50%

67) 38%

68) 6.4%

69) 5/8

70) .67232

Probability

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