Probability and Statistics
Grade 4
1. How many different arrangements of the letters “MATH” are possible?
2. What is the probability that a randomly chosen letter from the phrase “A quick brown fox jumped
over the lazy dog” is a vowel? (Assume “y” is a vowel here.) Express your answer as a common
fraction.
3. If there are seven blue socks, three yellow socks, and twelve red socks mixed randomly in a
drawer, how many socks do you need to draw to make sure you have at least one pair of the same
color socks?
4. If two coins are flipped, what is the probability that both are heads?
5. As a joke on his teacher, Bobby decided to change the numbers on her six-sided die. He changed
the numbers one through six to 2, 4, 5, 7, 8, and 9. If she now rolls the die, what is the probability
that a number greater than six will show up and thus will confuse his teacher?
6. If your score on the first test was 70%, your score on the second test was 90%, and you want to
receive a 80% in the class overall, what score must you get on the third test? (Assume all tests are
weighted equally.)
7. If I have three different pairs of sneakers, six different t-shirts, four different pairs of shorts and
two different hats, how many combinations of one pair of sneakers, one t-shirt, one pair of shorts,
and one hat are possible?
8. How many passwords are possible if each of the passwords must consist of four different
numbers?
9. Suppose there are 500 students at a local math competition. 400 of them like algebra, 120 of them
like geometry and 40 like both. How many students like neither algebra nor geometry?
10. If you are playing a game in which you can score either three or five points at a time, how many
different ways would there be to score 23 points?
Probability and Statistics
Grade 5
1. If there are seven blue socks, three yellow socks, and twelve red socks mixed randomly in a
drawer, how many socks do you need to draw to make sure you have at least one pair of the same
color socks?
2. If two coins are flipped, what is the probability that both are heads?
3. As a joke on his teacher, Bobby decided to change the numbers on her six-sided die. He changed
the numbers one through six to 2, 4, 5, 7, 8, and 9. If she now rolls the die, what is the probability
that a number greater than six will show up and thus will confuse his teacher?
4. If your score on the first test was 70%, your score on the second test was 90%, and you want to
receive a 80% in the class overall, what score must you get on the third test? (Assume all tests are
weighted equally.)
5. If I have three different pairs of sneakers, six different t-shirts, four different pairs of shorts and
two different hats, how many combinations of one pair of sneakers, one t-shirt, one pair of shorts,
and one hat are possible?
6. How many passwords are possible if each of the passwords must consist of four different
numbers?
7. Suppose there are 500 students at a local math competition. 400 of them like algebra, 120 of them
like geometry and 40 like both. How many students like neither algebra nor geometry?
8. If you are playing a game in which you can score either three or five points at a time, how many
different ways would there be to score 23 points?
9.
What is the median in the following set of percentages?
43%, 25%, 19%, 44%, 22%, 39%, 74%, 22%, 93%, 85%, 24%, 22%, 67%
10. A committee of three students needs to be made from six students who applied for the positions. If
each of the three positions is the exact same (the order in which they are chosen does not matter),
how many ways would there be to pick the committee from those who applied?
Probability and Statistics
Grade 6
1. As a joke on his teacher, Bobby decided to change the numbers on her six-sided die. He changed
the numbers one through six to 2, 4, 5, 7, 8, and 9. If she now rolls the die, what is the probability
that a number greater than six will show up and thus will confuse his teacher?
2. If your score on the first test was 70%, your score on the second test was 90%, and you want to
receive a 80% in the class overall, what score must you get on the third test? (Assume all tests are
weighted equally.)
3. If I have three different pairs of sneakers, six different t-shirts, four different pairs of shorts and
two different hats, how many combinations of one pair of sneakers, one t-shirt, one pair of shorts,
and one hat are possible?
4. How many passwords are possible if each of the passwords must consist of four different
numbers?
5. Suppose there are 500 students at a local math competition. 400 of them like algebra, 120 of them
like geometry and 40 like both. How many students like neither algebra nor geometry?
6. If you are playing a game in which you can score either three or five points at a time, how many
different ways would there be to score 23 points?
7.
What is the median in the following set of percentages?
43%, 25%, 19%, 44%, 22%, 39%, 74%, 22%, 93%, 85%, 24%, 22%, 67%
8.
A committee of three students needs to be made from six students who applied for the positions. If
each of the three positions is the exact same (the order in which they are chosen does not matter),
how many ways would there be to pick the committee from those who applied?
9. If three cards are drawn (and then replaced) from a standard fifty-two card deck, what is the
probability that the first card will be a black ace, the second card a black card, and the final card a
red card? Express your answer as a common fraction.
10. If the probability of having a massive snowstorm on any given day in Snowyville is 65%, the
probability of having a snowstorm and a windstorm is 20%, and the probability of having a
windstorm is 35%, what is the probability of having a snowstorm or a windstorm? Express your
answer to the nearest percent.
Probability and Statistics
Grade 7
1. If I have three different pairs of sneakers, six different t-shirts, four different pairs of shorts and
two different hats, how many combinations of one pair of sneakers, one t-shirt, one pair of shorts,
and one hat are possible?
2. How many passwords are possible if each of the passwords must consist of four different
numbers?
3. Suppose there are 500 students at a local math competition. 400 of them like algebra, 120 of them
like geometry and 40 like both. How many students like neither algebra nor geometry?
4. If you are playing a game in which you can score either three or five points at a time, how many
different ways would there be to score 23 points?
5.
What is the median in the following set of percentages?
43%, 25%, 19%, 44%, 22%, 39%, 74%, 22%, 93%, 85%, 24%, 22%, 67%
6.
A committee of three students needs to be made from six students who applied for the positions. If
each of the three positions is the exact same (the order in which they are chosen does not matter),
how many ways would there be to pick the committee from those who applied?
7. If three cards are drawn (and then replaced) from a standard fifty-two card deck, what is the
probability that the first card will be a black ace, the second card a black card, and the final card a
red card? Express your answer as a common fraction.
8. If the probability of having a massive snowstorm on any given day in Snowyville is 65%, the
probability of having a snowstorm and a windstorm is 20%, and the probability of having a
windstorm is 35%, what is the probability of having a snowstorm or a windstorm? Express your
answer to the nearest percent.
9. Two fair dice are tossed onto a table. You decide to add the numbers up and do that many jumping
jacks. What is the probability that you will be doing an even number of jumping jacks? Express
your answer as a common fraction.
10. What is the mean of the following three values?
• The number of one-digit prime numbers,
• The number of two-digit perfect squares,
• The number of three-digit multiples of 100.
Round your answer to the nearest tenth.
Probability and Statistics
Grade 8
1. Suppose there are 500 students at a local math competition. 400 of them like algebra, 120 of them
like geometry and 40 like both. How many students like neither algebra nor geometry?
2. If you are playing a game in which you can score either three or five points at a time, how many
different ways would there be to score 23 points?
3.
What is the median in the following set of percentages?
43%, 25%, 19%, 44%, 22%, 39%, 74%, 22%, 93%, 85%, 24%, 22%, 67%
4.
A committee of three students needs to be made from six students who applied for the positions. If
each of the three positions is the exact same (the order in which they are chosen does not matter),
how many ways would there be to pick the committee from those who applied?
5. If three cards are drawn (and then replaced) from a standard fifty-two card deck, what is the
probability that the first card will be a black ace, the second card a black card, and the final card a
red card? Express your answer as a common fraction.
6. If the probability of having a massive snowstorm on any given day in Snowyville is 65%, the
probability of having a snowstorm and a windstorm is 20%, and the probability of having a
windstorm is 35%, what is the probability of having a snowstorm or a windstorm? Express your
answer to the nearest percent.
7. Two fair dice are tossed onto a table. You decide to add the numbers up and do that many jumping
jacks. What is the probability that you will be doing an even number of jumping jacks? Express
your answer as a common fraction.
8. What is the mean of the following three values?
• The number of one-digit prime numbers,
• The number of two-digit perfect squares,
• The number of three-digit multiples of 100.
Round your answer to the nearest tenth.
9. How many different arrangements of the letters “PROBABILITY” are possible?
10. To amaze your friends with your “magic” skills, you take a standard deck of cards and have one
of them randomly pick a card. You then tell them to memorize what denomination (i.e. 7, 8, 9,
king, ace, etc…) of card they have, and then rip the card up. What is the probability that the next
two cards you draw from the deck without replacement are also of the same denomination? (And
thus will shock and amaze your friends)