Probability and stats Practice problems
Students are learning about probability. The teacher explains the theoretical probability of a two-sided
coin landing on any one side. Students then work in groups and flip a two-sided coin several times. The
first group of students flips the coin 20 times and finds the coin lands on side A 13 times and side B 7
times. Which of the following observations, based on the scenario, about probability is accurate?
Correct Answer: The theoretical probability of the coin landing on side A is less than the experimental
results recorded.
Rohan rolls a 10 sided dice with sides numbered from 1 to 10. What is the probability that he rolls a
prime number? Correct Answer: 2/5
The data table shown describes how students get to school each morning at Memorial Middle School. If
a student is drawn at random from the walkers and bus riders, what is the probability they are a walker?
Correct Answer: 7/44
A student tosses a six-sided die, with each side numbered 1 through 6, and flips a coin. What is the
probability that the die will land on the face numbered 1 and the coin will land showing tails? Correct
Answer: 1/12
Brianna spun each of the two spinners. Which expression depicts the probability she spins an "A" on the
first spinner and a "1" on the second? Correct Answer: 1/3 • 1/4
Brianna spun each of the two spinners. What is the probability that she did NOT spin a "1" on the second
spinner? Correct Answer: 3/4
Rae Anne has 3 children. The first is a boy, the second is a boy, and the third is a boy. What is the
probability that her fourth child is also a boy? Correct Answer: 1/2
Of the 40 prizes in the toy box, 15 are slime, 18 are fidget spinners, and 7 are candy. If a student reaches
in the box and randomly draws a prize, what are the odds it is not slime? Correct Answer: 5/8
The local radio station is giving away free concert tickets to the 104th person who calls in. Andrew and
John want to win the concert tickets, so Andrew calls into the station 6 times and John calls in xx times.
If the probability that either Andrew or John wins the concert tickets is 0.125, what is the value of xx?
Correct Answer: 7
Whitney is packing for a week-long trip. She fills her suitcase with 5 shirts, 3 pairs of pants, 2 skirts, and
2 dresses. If an outfit consists of 1 shirt and 1 bottom (pant or skirt) or 1 dress, how many different
outfits can Whitney create? Correct Answer: 27
Mrs. Spiser is teaching students about populations and samples in mathematics. They will take a survey
to see how many students are buying lunch in the cafeteria from the sample and then they will compare
it to the whole class. What is the best method to use? Correct Answer: As students enter her room, they
randomly draw a red or black card. She teaches the concept by explaining that the class is the
population and students who drew a red card are the sample group.
,Students in Mr. Miller's class are given a worksheet with the different combinations that can be reached
when flipping a coin and rolling a standard die. Students then work in pairs to flip and roll all of the
combinations. What topic is Mr. Miller teaching Correct Answer: sample space
A teacher carries around a bag of marbles with 10 of each of the following colors: blue, white, and
yellow. She asks students to draw one marble from the bag. Before they draw, they must state the
probability of drawing a certain color. The first student says the probability of drawing a blue is 1 out of
3 because 10 out of 30 simplifies to 1:3. The student holds onto his blue marble and the next student
says his probability of drawing yellow is 1:3. Evaluate his statement. Correct Answer: It is incorrect and
a common misconception about dependent events.
Mrs. Harris writes all the numbers from 4 to 24 on slips of paper and places them in a hat. She then asks
a student to pick a number from the hat. What is the probability that the number chosen by the student
will be a prime number? Correct Answer: 1/3
A student was selected as a captain of a cooking team in a consumer and family studies class. The
student could pick 2 of 5 girls and 3 of 7 boys to be on their team. What is the total number of different
teams that this captain could select? Correct Answer: 350
John creates a probability model for rolling two six-sided die as shown above. The value of each die is on
the outside, the sum of the two is on the inside. What is the probability of rolling two dice and having a
sum of 4? Correct Answer: 1/12
Sally and Susie place 30 white marbles and 9 black marbles in a sack. They play a game where the object
of the game is to accumulate more white marbles than the other person. On each turn a person can take
as many marbles as they would like, but if they grab a black marble then they must return all their
marbles taken on that turn. On Sally's turn she picks up 3 white marbles and no black marbles. If Susie
grabs one more marble, what are the odds that she will grab a black marble? (Note: Sally does not
return her 3 marbles to the sack.) Correct Answer: 1 in 4
What is the probability that the sum of the two dice is between 2 and 12, inclusive? Correct Answer: 1
10 groups of 5 students spin the spinner shown. If each student spins the spinner 6 times, what is the
expected number of times the spinner would land on A for all 10 groups of students? There is an equal
chance the spinner lands on A, B, or C. Correct Answer: 100
The formula for permutations is: nPr = \frac{n!}{ \left( n-r \right) !}
(n−r)!
n!
while the formula for combinations is: nCr= \frac{n!}{r! \left( n-r \right) !}
r!(n−r)!
n!
.
, As a warm-up, Ms. Caulkins asks her students to compare these two formulas and identify the
differences and similarities before she has taught what the formulas are used for. What is her goal in
this exercise? Correct Answer: activating prior knowledge of reducing fractions
Michelle is assigned homework to flip a coin 10 times, then 100 times, then 1000 times. She decides to
use a use her computer to generate a 1 for heads or a 2 for tails. She has the following results:
Number Of Trials
Number of Heads (1s)
Number of Tails (2s)
10
7
3
100
45
55
1000
507
493
What can be said about the results of her simulation? Correct Answer: As she performed more trials,
the experimental probability became closer to the theoretical probability.
A 6-sided die is rolled 100 times with the results shown in the table.
Outcome
1
2
3
4
5
Students are learning about probability. The teacher explains the theoretical probability of a two-sided
coin landing on any one side. Students then work in groups and flip a two-sided coin several times. The
first group of students flips the coin 20 times and finds the coin lands on side A 13 times and side B 7
times. Which of the following observations, based on the scenario, about probability is accurate?
Correct Answer: The theoretical probability of the coin landing on side A is less than the experimental
results recorded.
Rohan rolls a 10 sided dice with sides numbered from 1 to 10. What is the probability that he rolls a
prime number? Correct Answer: 2/5
The data table shown describes how students get to school each morning at Memorial Middle School. If
a student is drawn at random from the walkers and bus riders, what is the probability they are a walker?
Correct Answer: 7/44
A student tosses a six-sided die, with each side numbered 1 through 6, and flips a coin. What is the
probability that the die will land on the face numbered 1 and the coin will land showing tails? Correct
Answer: 1/12
Brianna spun each of the two spinners. Which expression depicts the probability she spins an "A" on the
first spinner and a "1" on the second? Correct Answer: 1/3 • 1/4
Brianna spun each of the two spinners. What is the probability that she did NOT spin a "1" on the second
spinner? Correct Answer: 3/4
Rae Anne has 3 children. The first is a boy, the second is a boy, and the third is a boy. What is the
probability that her fourth child is also a boy? Correct Answer: 1/2
Of the 40 prizes in the toy box, 15 are slime, 18 are fidget spinners, and 7 are candy. If a student reaches
in the box and randomly draws a prize, what are the odds it is not slime? Correct Answer: 5/8
The local radio station is giving away free concert tickets to the 104th person who calls in. Andrew and
John want to win the concert tickets, so Andrew calls into the station 6 times and John calls in xx times.
If the probability that either Andrew or John wins the concert tickets is 0.125, what is the value of xx?
Correct Answer: 7
Whitney is packing for a week-long trip. She fills her suitcase with 5 shirts, 3 pairs of pants, 2 skirts, and
2 dresses. If an outfit consists of 1 shirt and 1 bottom (pant or skirt) or 1 dress, how many different
outfits can Whitney create? Correct Answer: 27
Mrs. Spiser is teaching students about populations and samples in mathematics. They will take a survey
to see how many students are buying lunch in the cafeteria from the sample and then they will compare
it to the whole class. What is the best method to use? Correct Answer: As students enter her room, they
randomly draw a red or black card. She teaches the concept by explaining that the class is the
population and students who drew a red card are the sample group.
,Students in Mr. Miller's class are given a worksheet with the different combinations that can be reached
when flipping a coin and rolling a standard die. Students then work in pairs to flip and roll all of the
combinations. What topic is Mr. Miller teaching Correct Answer: sample space
A teacher carries around a bag of marbles with 10 of each of the following colors: blue, white, and
yellow. She asks students to draw one marble from the bag. Before they draw, they must state the
probability of drawing a certain color. The first student says the probability of drawing a blue is 1 out of
3 because 10 out of 30 simplifies to 1:3. The student holds onto his blue marble and the next student
says his probability of drawing yellow is 1:3. Evaluate his statement. Correct Answer: It is incorrect and
a common misconception about dependent events.
Mrs. Harris writes all the numbers from 4 to 24 on slips of paper and places them in a hat. She then asks
a student to pick a number from the hat. What is the probability that the number chosen by the student
will be a prime number? Correct Answer: 1/3
A student was selected as a captain of a cooking team in a consumer and family studies class. The
student could pick 2 of 5 girls and 3 of 7 boys to be on their team. What is the total number of different
teams that this captain could select? Correct Answer: 350
John creates a probability model for rolling two six-sided die as shown above. The value of each die is on
the outside, the sum of the two is on the inside. What is the probability of rolling two dice and having a
sum of 4? Correct Answer: 1/12
Sally and Susie place 30 white marbles and 9 black marbles in a sack. They play a game where the object
of the game is to accumulate more white marbles than the other person. On each turn a person can take
as many marbles as they would like, but if they grab a black marble then they must return all their
marbles taken on that turn. On Sally's turn she picks up 3 white marbles and no black marbles. If Susie
grabs one more marble, what are the odds that she will grab a black marble? (Note: Sally does not
return her 3 marbles to the sack.) Correct Answer: 1 in 4
What is the probability that the sum of the two dice is between 2 and 12, inclusive? Correct Answer: 1
10 groups of 5 students spin the spinner shown. If each student spins the spinner 6 times, what is the
expected number of times the spinner would land on A for all 10 groups of students? There is an equal
chance the spinner lands on A, B, or C. Correct Answer: 100
The formula for permutations is: nPr = \frac{n!}{ \left( n-r \right) !}
(n−r)!
n!
while the formula for combinations is: nCr= \frac{n!}{r! \left( n-r \right) !}
r!(n−r)!
n!
.
, As a warm-up, Ms. Caulkins asks her students to compare these two formulas and identify the
differences and similarities before she has taught what the formulas are used for. What is her goal in
this exercise? Correct Answer: activating prior knowledge of reducing fractions
Michelle is assigned homework to flip a coin 10 times, then 100 times, then 1000 times. She decides to
use a use her computer to generate a 1 for heads or a 2 for tails. She has the following results:
Number Of Trials
Number of Heads (1s)
Number of Tails (2s)
10
7
3
100
45
55
1000
507
493
What can be said about the results of her simulation? Correct Answer: As she performed more trials,
the experimental probability became closer to the theoretical probability.
A 6-sided die is rolled 100 times with the results shown in the table.
Outcome
1
2
3
4
5
