Download WCMC Probability and Statistics `10 FD

Probability and
Statistics
Grade 4
Grade 4
1. What is the probability of rolling an even number on a standard, fair, six-sided die? Express your
answer as a reduced fraction.
2. What is the probability that a randomly selected two-digit number will be a multiple of nine?
Express your answer as a reduced fraction.
Use the following list of heights of eighteen fourth grade class for problems #3 and #4
63 in, 55in, 56in, 45in, 54in, 55in, 55in, 57in, 54in, 52in, 53in, 50in, 52in, 53in, 52in, 60in, 55in, 51in
3. If you do not include the tallest and shortest person in the class, what is the mean height?
4. What is the sum of the mode and the median of the class heights?
5. Suppose your math teacher just washed and dried all of her dirty socks – 14 of which are white, 4
of which are black, and 9 of which are colored. If she selects a random sock from the drier, what
is the probability that she will not choose a black sock? Express your answer as a reduced
fraction.
1
6. If the probability of winning a board game is equal to 8 and the probability of not winning the
3
card game is 5 , what is the probability of winning both the board game and the card game?
Assume the probabilities of winning the games are independent. Express your answer as a
reduced fraction.
7. If fourteen students in the class received 75% on a test and six students in a class received 95% on
the same test, what was the average percentage score on the test?
8.
Brianna has just moved into her new house and has four checks written for unique amounts of
money that she filled out completely except for the names of the four companies receiving the
money. If she randomly puts the names of the checks, what is the probability she will write the
correct company on every check? Express your answer as a reduced fraction.
9. Many students believe that if you do not know the answer to a multiple choice problem during a
test, that guessing the choice “c” will give you the best chance of doing well. If you decide to try
that technique out and guess “c” on a five question test where each question has four choices, what
is the probability that you will answer all five questions correctly? Express your answer as a
reduced fraction.
10. If the average of twelve positive integers is 15, and each integer is different, what is the largest
one of the twelve integers could be?
Probability and
Statistics
Grade 5
Grade 5
Use the following list of heights of eighteen fourth grade class for problems #1 and #2
63 in, 55in, 56in, 45in, 54in, 55in, 55in, 57in, 54in, 52in, 53in, 50in, 52in, 53in, 52in, 60in, 55in, 51in
1. If you do not include the tallest and shortest person in the class, what is the mean height?
2. What is the sum of the mode and the median of the class heights?
3. Suppose your math teacher just washed and dried all of her dirty socks – 14 of which are white, 4
of which are black, and 9 of which are colored. If she selects a random sock from the drier, what
is the probability that she will not choose a black sock? Express your answer as a reduced
fraction.
1
4. If the probability of winning a board game is equal to 8 and the probability of not winning the
3
card game is 5 , what is the probability of winning both the board game and the card game?
Assume the probabilities of winning the games are independent. Express your answer as a
reduced fraction.
5. If fourteen students in the class received 75% on a test and six students in a class received 95% on
the same test, what was the average percentage score on the test?
6.
Brianna has just moved into her new house and has four checks written for unique amounts of
money that she filled out completely except for the names of the four companies receiving the
money. If she randomly puts the names of the checks, what is the probability she will write the
correct company on every check? Express your answer as a reduced fraction.
7. Many students believe that if you do not know the answer to a multiple choice problem during a
test, that guessing the choice “c” will give you the best chance of doing well. If you decide to try
that technique out and guess “c” on a five question test where each question has four choices, what
is the probability that you will answer all five questions correctly? Express your answer as a
reduced fraction.
8.
If the average of twelve positive integers is 15, and each integer is different, what is the largest
one of the twelve integers could be?
9.
Three of the five numbers in a set of data are 10, 65, and 75. If the mean of the data is 50 and the
range of the data is 65, what is the largest that the median could be if each piece of data must be a
positive integer?
Probability and
Statistics
Grade 5
Grade 5
10. The numbers 1, 2, 3, and 4 are placed into a box. Three of the numbers are randomly chosen from
the box one at a time and used to create a three digit number where the first number drawn is the
first digit, the second number is the second digit, and the third number is the third digit, what is the
probability the three-digit number will be divisible by three? Express your answer as a reduced
fraction.
Probability and
Statistics
Grade 6
1. Suppose your math teacher just washed and dried all of her dirty socks – 14 of which are white, 4
of which are black, and 9 of which are colored. If she selects a random sock from the drier, what
is the probability that she will not choose a black sock? Express your answer as a reduced
fraction.
1
2. If the probability of winning a board game is equal to 8 and the probability of not winning the
3
card game is 5 , what is the probability of winning both the board game and the card game?
Assume the probabilities of winning the games are independent. Express your answer as a
reduced fraction.
3. If fourteen students in the class received 75% on a test and six students in a class received 95% on
the same test, what was the average percentage score on the test?
4.
Brianna has just moved into her new house and has four checks written for unique amounts of
money that she filled out completely except for the names of the four companies receiving the
money. If she randomly puts the names of the checks, what is the probability she will write the
correct company on every check? Express your answer as a reduced fraction.
5. Many students believe that if you do not know the answer to a multiple choice problem during a
test, that guessing the choice “c” will give you the best chance of doing well. If you decide to try
that technique out and guess “c” on a five question test where each question has four choices, what
is the probability that you will answer all five questions correctly? Express your answer as a
reduced fraction.
6.
If the average of twelve positive integers is 15, and each integer is different, what is the largest
one of the twelve integers could be?
7.
Three of the five numbers in a set of data are 10, 65, and 75. If the mean of the data is 50 and the
range of the data is 65, what is the largest that the median could be if each piece of data must be a
positive integer?
8. The numbers 1, 2, 3, and 4 are placed into a box. Three of the numbers are randomly chosen from
the box one at a time and used to create a three digit number where the first number drawn is the
first digit, the second number is the second digit, and the third number is the third digit, what is the
probability the three-digit number will be divisible by three? Express your answer as a reduced
fraction.
9.
In search for the ancient mathematics knowledge that has been lost since 3141BC, explorers have
come to a vault which requires them to place two numbers in the first two spots and two letters in
the other two spots. If they can try 200 combinations an hour, how many hours will it take to go
through all the possible combinations?
Probability and
Statistics
Grade 6
10. If you were to flip five fair coins, what is the probability that at least one of them would be heads?
Express your answer as a reduced fraction.
Probability and
Statistics
Grade 7
1. If fourteen students in the class received 75% on a test and six students in a class received 95% on
the same test, what was the average percentage score on the test?
2.
Brianna has just moved into her new house and has four checks written for unique amounts of
money that she filled out completely except for the names of the four companies receiving the
money. If she randomly puts the names of the checks, what is the probability she will write the
correct company on every check? Express your answer as a reduced fraction.
3. Many students believe that if you do not know the answer to a multiple choice problem during a
test, that guessing the choice “c” will give you the best chance of doing well. If you decide to try
that technique out and guess “c” on a five question test where each question has four choices, what
is the probability that you will answer all five questions correctly? Express your answer as a
reduced fraction.
4.
If the average of twelve positive integers is 15, and each integer is different, what is the largest
one of the twelve integers could be?
5. Three of the five numbers in a set of data are 10, 65, and 75. If the mean of the data is 50 and the
range of the data is 65, what is the largest that the median could be if each piece of data must be a
positive integer?
6. The numbers 1, 2, 3, and 4 are placed into a box. Three of the numbers are randomly chosen from
the box one at a time and used to create a three digit number where the first number drawn is the
first digit, the second number is the second digit, and the third number is the third digit, what is the
probability the three-digit number will be divisible by three? Express your answer as a reduced
fraction.
7.
In search for the ancient mathematics knowledge that has been lost since 3141BC, explorers have
come to a vault which requires them to place two numbers in the first two spots and two letters in
the other two spots. If they can try 200 combinations an hour, how many hours will it take to go
through all the possible combinations?
8.
If you were to flip five fair coins, what is the probability that at least one of them would be heads?
Express your answer as a reduced fraction.
9.
How many unique arrangements of the letters “TWENTYTEN” are possible?
10. At some strange math competition held in the Northwest, there are four unique team tests, a mental
math test, and an individual test. If the only guideline for the order of the tests is that the
individual test must come either right before or right after the mental math test, how many possible
orders for the competitions are there?
Probability and
Statistics
Grade 8
1. Many students believe that if you do not know the answer to a multiple choice problem during a
test, that guessing the choice “c” will give you the best chance of doing well. If you decide to try
that technique out and guess “c” on a five question test where each question has four choices,
what is the probability that you will answer all five questions correctly? Express your answer
as a reduced fraction.
2.
If the average of twelve positive integers is 15, and each integer is different, what is the largest
one of the twelve integers could be?
3.
Three of the five numbers in a set of data are 10, 65, and 75. If the mean of the data is 50 and the
range of the data is 65, what is the largest that the median could be if each piece of data must be a
positive integer?
4. The numbers 1, 2, 3, and 4 are placed into a box. Three of the numbers are randomly chosen from
the box one at a time and used to create a three digit number where the first number drawn is the
first digit, the second number is the second digit, and the third number is the third digit, what is the
probability the three-digit number will be divisible by three? Express your answer as a reduced
fraction.
5.
In search for the ancient mathematics knowledge that has been lost since 3141BC, explorers have
come to a vault which requires them to place two numbers in the first two spots and two letters in
the other two spots. If they can try 200 combinations an hour, how many hours will it take to go
through all the possible combinations?
6.
If you were to flip five fair coins, what is the probability that at least one of them would be heads?
Express your answer as a reduced fraction.
7.
How many unique arrangements of the letters “TWENTYTEN” are possible?
8. At some strange math competition held in the Northwest, there are four unique team tests, a mental
math test, and an individual test. If the only guideline for the order of the tests is that the
individual test must come either right before or right after the mental math test, how many possible
orders for the competitions are there?
9. An amateur magician wants to do a “trick” by guessing the correct color of the marble he draws.
The first bag contains three white and five red marbles, and the second bag contains one white and
six red marbles. If he first takes a random marble from the first bag and puts it into the second
bag, what is the probability that he will draw a red from the second bag? Express your answer as
a reduced fraction.
Probability and
Statistics
Grade 8
10. What is the probability of dealing a five-card poker hand where the result is a two-pair? A two-pair
is where there are two unique pairs of cards that are the same, and a fifth card that is different from
both of the pairs (i.e. 5 5 4 4 3 or K K J 9 J but not 2 2 2 2 A). Express your answer as a
decimal to the nearest hundredth.