Probability and Statistics
5th Grade
Bubble in your answers on the answer sheet. Be sure to erase all mistakes completely. You do not need
to bubble in leading zeros – the answer of “7” does not need to be answered as “007”. If your answer is a
fraction like
, bubble in 316.
1. 2 points: The classic sock drawer contains twelve black socks, three blue socks, and five white
socks. If you choose a sock at random, what is the probability that a black sock or a blue sock
will be chosen? Express your answer as a reduced fraction.
The following information is needed to solve problems 2 and 3.
Two teachers, one from Room 5, and one from Room 2, polled each of their classes to see how many
siblings each student has. Use the following graphs that they came up with to answer questions #2
and #3.
2. 2 points: How many more students were polled from Room 2 than Room 5?
3. 2 points: What is the positive difference between Room 5’s and Room 2’s average number of
siblings per student? Express your answer to the nearest hundredth.
4. 3 points: At the end of the year, during which there were 10 grueling mathematics tests,
Grisham's average score was 70%. When looking at his final test though, he noticed there was a
grading error which would raise that test's score from the original score of 40% to a new score of
70%. If all ten tests are weighted equally, what is his new average score for the year? Express
your answer as a percent.
5. 3 points: A mathematician wants to create a four-digit password for his computer using three
rules:
• The first and last digits must be prime numbers.
• The second digit must be odd.
• The third digit can be any digit but cannot be a repeat of the second digit.
How many unique passwords are possible?
Probability and Statistics
5th Grade
6. 3 points: Suppose that eight students' scores on a 100-point test are: 20, 44, 75, 70, 100, 88, 95,
and 68. What is the probability that a randomly selected student will have scored below the class
average? Express your answer as a reduced fraction.
7. 3 points: The principal at Einstein High had seen all sorts of colorful rubber bands lying on the
grounds, so she decided to find out how many of the 100 students were playing with two of the
most popular toys. She found that 42 students played with Tech Decks, 25 played with Silly
Bandz, and 22 played with both. How many students played with neither the Tech Decks nor
Silly Bandz?
8. 4 points: How many ways are there to select a student body president, vice-president, and
treasurer from a group of eight candidates?
9. 4 points: In the board game Monopoly, you roll two dice to determine the number of spaces you
move. If you roll “doubles”, that is, the same number on each die, you get an extra turn.
Assuming you are rolling two fair six-sided dice, what is the probability of rolling doubles on any
given turn? Express your answer as a reduced fraction.
10. 4 points: Suppose that two positive integers less than or equal to 1000 are selected randomly and
with replacement. What is probability that the product of those two integers will be odd?
Express your answer as a reduced fraction.
Probability and Statistics
6th Grade
Bubble in your answers on the answer sheet. Be sure to erase all mistakes completely. You do not need
to bubble in leading zeros – the answer of “7” does not need to be answered as “007”. If your answer is a
fraction like
, bubble in 316.
1. 2 points: At the end of the year, during which there were 10 grueling mathematics tests,
Grisham's average score was 70%. When looking at his final test though, he noticed there was a
grading error which would raise that test's score from the original score of 40% to a new score of
70%. If all ten tests are weighted equally, what is his new average score for the year? Express
your answer as a percent.
2. 2 points: A mathematician wants to create a four-digit password for his computer using three
rules:
• The first and last digits must be prime numbers.
• The second digit must be odd.
• The third digit can be any digit but cannot be a repeat of the second digit.
How many unique passwords are possible?
3. 2 points: Suppose that eight students' scores on a 100-point test are: 20, 44, 75, 70, 100, 88, 95,
and 68. What is the probability that a randomly selected student will have scored below the class
average? Express your answer as a reduced fraction.
4. 3 points: The principal at Einstein High had seen all sorts of colorful rubber bands lying on the
grounds, so she decided to find out how many of the 100 students were playing with two of the
most popular toys. She found that 42 students played with Tech Decks, 25 played with Silly
Bandz, and 22 played with both. How many students played with neither the Tech Decks nor
Silly Bandz?
5. 3 points: How many ways are there to select a student body president, vice-president, and
treasurer from a group of eight candidates?
6. 3 points: In the board game Monopoly, you roll two dice to determine the number of spaces you
move. If you roll “doubles”, that is, the same number on each die, you get an extra turn.
Assuming you are rolling two fair six-sided dice, what is the probability of rolling doubles on any
given turn? Express your answer as a reduced fraction.
7. 3 points: Suppose that two positive integers less than or equal to 1000 are selected randomly and
with replacement. What is probability that the product of those two integers will be odd?
Express your answer as a reduced fraction.
Probability and Statistics
6th Grade
8. 4 points: Suppose that two brothers, Edward and Carlos, had a coin flip-off to see who would do
the evening chores. Whoever flipped the least heads after three flips would have to do the chores.
If they tied, they would share the work. However, Edward didn't realize that he had a weighted
coin that landed on heads 30% of the time. If Carlos flipped three heads, what is the probability
that Edward would have to do the chores by himself? Express your answer to the nearest
whole percent.
9. 4 points: If six fair coins are flipped, what is the probability that more than half of the coins will
land on heads? Express your answer to the nearest whole percent.
10. 4 points: How many unique arrangements are possible with the letters in the word “BIEBER”?
Probability and Statistics
7th Grade
Bubble in your answers on the answer sheet. Be sure to erase all mistakes completely. You do not need
to bubble in leading zeros – the answer of “7” does not need to be answered as “007”. If your answer is a
fraction like
, bubble in 316.
1. 2 points: The principal at Einstein High had seen all sorts of colorful rubber bands lying on the
grounds, so she decided to find out how many of the 100 students were playing with two of the
most popular toys. She found that 42 students played with Tech Decks, 25 played with Silly
Bandz, and 22 played with both. How many students played with neither the Tech Decks nor
Silly Bandz?
2. 2 points: How many ways are there to select a student body president, vice-president, and
treasurer from a group of eight candidates?
3. 2 points: In the board game Monopoly, you roll two dice to determine the number of spaces you
move. If you roll “doubles”, that is, the same number on each die, you get an extra turn.
Assuming you are rolling two fair six-sided dice, what is the probability of rolling doubles on any
given turn? Express your answer as a reduced fraction.
4. 3 points: Suppose that two positive integers less than or equal to 1000 are selected randomly and
with replacement. What is probability that the product of those two integers will be odd?
Express your answer as a reduced fraction.
5. 3 points: Suppose that two brothers, Edward and Carlos, had a coin flip-off to see who would do
the evening chores. Whoever flipped the least heads after three flips would have to do the chores.
If they tied, they would share the work. However, Edward didn't realize that he had a weighted
coin that landed on heads 30% of the time. If Carlos flipped three heads, what is the probability
that Edward would have to do the chores by himself? Express your answer to the nearest
whole percent.
6. 3 points: If six fair coins are flipped, what is the probability that more than half of the coins will
land on heads? Express your answer to the nearest whole percent.
7. 3 points: How many unique arrangements are possible with the letters in the word “BIEBER”?
8. 4 points: A family is gathering to take pictures of four generations at once. The oldest generation
– Andrew and Mike – each had two kids, each of which had three kids, each of which had four
kids. If only the aforementioned people were at the gathering, how many people were there in all?
9. 4 points: At your birthday party, a group of friends devise a game for you to play. They line up 7
party hats, 2 of which have balls underneath them. You win the game if you choose the two hats
with the balls underneath within the first three choices. What is the probability you will win the
game? Express your answer as a reduced fraction.
Probability and Statistics
7th Grade
10. 4 points: In a double elimination tournament, teams continue playing until they have lost two
games. If there are eight teams in one particular double elimination tournament, what is the
maximum number of games that will have to be played to determine a winner?
Probability and Statistics
8th Grade
Bubble in your answers on the answer sheet. Be sure to erase all mistakes completely. You do not need
to bubble in leading zeros – the answer of “7” does not need to be answered as “007”. If your answer is a
fraction like
, bubble in 316.
1. 2 points: Suppose that two positive integers less than or equal to 1000 are selected randomly and
with replacement. What is probability that the product of those two integers will be odd?
Express your answer as a reduced fraction.
2. 2 points: Suppose that two brothers, Edward and Carlos, had a coin flip-off to see who would do
the evening chores. Whoever flipped the least heads after three flips would have to do the chores.
If they tied, they would share the work. However, Edward didn't realize that he had a weighted
coin that landed on heads 30% of the time. If Carlos flipped three heads, what is the probability
that Edward would have to do the chores by himself? Express your answer to the nearest
whole percent.
3. 2 points: If six fair coins are flipped, what is the probability that more than half of the coins will
land on heads? Express your answer to the nearest whole percent.
4. 3 points: How many unique arrangements are possible with the letters in the word “BIEBER”?
5. 3 points: A family is gathering to take pictures of four generations at once. The oldest generation
– Andrew and Mike – each had two kids, each of which had three kids, each of which had four
kids. If only the aforementioned people were at the gathering, how many people were there in all?
6. 3 points: At your birthday party, a group of friends devise a game for you to play. They line up 7
party hats, 2 of which have balls underneath them. You win the game if you choose the two hats
with the balls underneath within the first three choices. What is the probability you will win the
game? Express your answer as a reduced fraction.
7. 3 points: In a double elimination tournament, teams continue playing until they have lost two
games. If there are eight teams in one particular double elimination tournament, what is the
maximum number of games that will have to be played to determine a winner?
8. 4 points: Suppose that an anti-virus software program successfully cleans a computer of all
viruses 40% of the time. If the software is loaded onto five computers, what is the probability that
it will clean exactly two computers successfully? Express your answer to the nearest whole
percent.
9. 4 points: In your coin pouch, you have six quarters, three dimes, three nickels, and eight pennies.
If you select two coins at random with replacement, what is the probability that you will have at
least $0.10? Express your answer as a decimal.
Probability and Statistics
8th Grade
10. 4 points: In the game of Blackjack, if you are dealt both an ace and either a King, Queen, Jack, or
ten, you have been dealt a “blackjack”. Assuming you are the only person being dealt two cards
from a standard 52-card deck, what is the probability that you will be dealt a blackjack? Express
your answer to the nearest whole percent.