SOPHIA STATISTICS UNIT 5 VIEW AHEAD
PAPER 2026 QUESTIONS WITH FULL ANSWERS
GRADED A+
◉ Sports science researchers determined that, for those people who
skateboard, 22% have never had an injury, 45% have had one injury,
18% have had two injuries, and 15% have had three or more
injuries. What is the probability that a randomly chosen
skateboarder has had one or two injuries? Answer: C. 0.63
◉ Three siblings, Peyton, Cameron, and Dakota, all ask their parents
to borrow the family car for different events around town. Since they
cannot all borrow the car at the same time, the parents decide to use
randomness to decide who gets the car. They will roll a single, fair,
six-sided number cube. Peyton gets the car if a 1 or 2 is rolled.
Cameron gets the car if a 3 or 4 is rolled, and Dakota gets the car if a
5 or 6 is rolled. Which of the following is the probability distribution
for who gets the car? Answer: (table) B. 1/3, 1/3, 1/3
◉ A movie enthusiast is going to select 1 of 4 movies (labeled W, X, Y,
and Z) using a random method where all the movies are equally
likely to be chosen. Which of the following is the probability
distribution for the movie selection? Answer: (table) C. 0.25, 0.25,
0.25, 0.25
,◉ Sports science researchers determined that, of those people who
skateboard, 22% have never had an injury, 45% have had one injury,
18% have had two injuries, and 15% have had three or more
injuries. What is the probability that a randomly chosen
skateboarder has not had three or more injuries? Answer: D. 0.85
◉ Some college advisors noticed the following breakdown of majors
for the incoming freshman at their school: 3% math, 22% nursing,
16% psychology, 11% criminal justice, and 48% business. Suppose a
first-year student was chosen at random. Which of the following is
the probability distribution for that student's major? Answer: (table)
B. 0.48, 0.11, 0.03, 0.22, 0.16
◉ A group of dental researchers are testing the effects of acidic
drinks on dental crowns. They have five containers of crowns
labeled V, W, X, Y, and Z. They will randomly select one of the
containers to be the control for the experiment by drawing one of
five well-mixed slips of paper with the same labels from a hat. Which
of the following is the probability model for the control container?
Answer: (table) A. 0.20, 0.20, 0.20, 0.20, 0.20
◉ 5-3 Applying Probability Rules Answer:
◉ A survey of 500 college students moving into their dorm revealed
that 425 brought a microwave, 380 brought a video game console,
and 50 brought neither a microwave nor a game console. A survey
participant is randomly selected. Let M be the event that the
,participant brought a microwave and let C be the event that the
participant brought a video game console. Organize these events in a
two-way table. What is the probability that the participant brought
both a microwave and a console, P(M and C)? Answer: B. 0.71
◉ A researcher asked 520 randomly selected people of three
different age groups (teen, young adult, and adult) about their
favorite music genre. The two-way table displays the distribution of
the responses.
A participant is randomly selected. Let C be the event that the
participant prefers country music and let T be the event that the
participant is a teen. What is the value of P(Cc and Tc)? Answer: C.
0.45
◉ Executives for a company that prints logos on products are
expanding the company's services to include souvenirs such as hats,
shirts, and foam fingers for sports teams. The data they collected
from a sample of 300 adults about their favorite sport to watch and
their favorite souvenir to buy are shown in the table.
A survey participant is randomly selected. Let F be the event that the
participant prefers football and let N be the event that the
participant prefers the foam finger. What is the value of P(F and N)?
Answer: A. 0.13
, ◉ In a survey given by camp counselors, campers were asked if they
like to swim and if they like to have a cookout. The Venn diagram
displays the campers' preferences.
A camper is selected at random. Let S be the event that the camper
likes to swim and let C be the event that the camper likes to have a
cookout. What is the probability that a randomly selected camper
likes to have a cookout? Answer: C. 0.93
◉ A survey of 500 college students moving into their dorm revealed
that 425 brought a microwave, 380 brought a video game console,
and 50 brought neither a microwave nor a game console. A survey
participant is randomly selected. Let M be the event that the
participant brought a microwave and let C be the event that the
participant brought a video game console. Organize these events in a
two-way table. What is the probability that the participant brought a
microwave or a console, P(M or C)? Answer: C. 0.90
◉ According to sales records at a local coffee shop, 75% of all
customers like hot coffee, 30% like iced coffee, and 22% like both
hot and iced coffee. The Venn diagram displays the coffee
preferences of the customers.
A randomly selected customer is asked if they like hot or iced coffee.
Let H be the event that the customer likes hot coffee and let I be the
event that the customer likes iced coffee. What is the probability that
PAPER 2026 QUESTIONS WITH FULL ANSWERS
GRADED A+
◉ Sports science researchers determined that, for those people who
skateboard, 22% have never had an injury, 45% have had one injury,
18% have had two injuries, and 15% have had three or more
injuries. What is the probability that a randomly chosen
skateboarder has had one or two injuries? Answer: C. 0.63
◉ Three siblings, Peyton, Cameron, and Dakota, all ask their parents
to borrow the family car for different events around town. Since they
cannot all borrow the car at the same time, the parents decide to use
randomness to decide who gets the car. They will roll a single, fair,
six-sided number cube. Peyton gets the car if a 1 or 2 is rolled.
Cameron gets the car if a 3 or 4 is rolled, and Dakota gets the car if a
5 or 6 is rolled. Which of the following is the probability distribution
for who gets the car? Answer: (table) B. 1/3, 1/3, 1/3
◉ A movie enthusiast is going to select 1 of 4 movies (labeled W, X, Y,
and Z) using a random method where all the movies are equally
likely to be chosen. Which of the following is the probability
distribution for the movie selection? Answer: (table) C. 0.25, 0.25,
0.25, 0.25
,◉ Sports science researchers determined that, of those people who
skateboard, 22% have never had an injury, 45% have had one injury,
18% have had two injuries, and 15% have had three or more
injuries. What is the probability that a randomly chosen
skateboarder has not had three or more injuries? Answer: D. 0.85
◉ Some college advisors noticed the following breakdown of majors
for the incoming freshman at their school: 3% math, 22% nursing,
16% psychology, 11% criminal justice, and 48% business. Suppose a
first-year student was chosen at random. Which of the following is
the probability distribution for that student's major? Answer: (table)
B. 0.48, 0.11, 0.03, 0.22, 0.16
◉ A group of dental researchers are testing the effects of acidic
drinks on dental crowns. They have five containers of crowns
labeled V, W, X, Y, and Z. They will randomly select one of the
containers to be the control for the experiment by drawing one of
five well-mixed slips of paper with the same labels from a hat. Which
of the following is the probability model for the control container?
Answer: (table) A. 0.20, 0.20, 0.20, 0.20, 0.20
◉ 5-3 Applying Probability Rules Answer:
◉ A survey of 500 college students moving into their dorm revealed
that 425 brought a microwave, 380 brought a video game console,
and 50 brought neither a microwave nor a game console. A survey
participant is randomly selected. Let M be the event that the
,participant brought a microwave and let C be the event that the
participant brought a video game console. Organize these events in a
two-way table. What is the probability that the participant brought
both a microwave and a console, P(M and C)? Answer: B. 0.71
◉ A researcher asked 520 randomly selected people of three
different age groups (teen, young adult, and adult) about their
favorite music genre. The two-way table displays the distribution of
the responses.
A participant is randomly selected. Let C be the event that the
participant prefers country music and let T be the event that the
participant is a teen. What is the value of P(Cc and Tc)? Answer: C.
0.45
◉ Executives for a company that prints logos on products are
expanding the company's services to include souvenirs such as hats,
shirts, and foam fingers for sports teams. The data they collected
from a sample of 300 adults about their favorite sport to watch and
their favorite souvenir to buy are shown in the table.
A survey participant is randomly selected. Let F be the event that the
participant prefers football and let N be the event that the
participant prefers the foam finger. What is the value of P(F and N)?
Answer: A. 0.13
, ◉ In a survey given by camp counselors, campers were asked if they
like to swim and if they like to have a cookout. The Venn diagram
displays the campers' preferences.
A camper is selected at random. Let S be the event that the camper
likes to swim and let C be the event that the camper likes to have a
cookout. What is the probability that a randomly selected camper
likes to have a cookout? Answer: C. 0.93
◉ A survey of 500 college students moving into their dorm revealed
that 425 brought a microwave, 380 brought a video game console,
and 50 brought neither a microwave nor a game console. A survey
participant is randomly selected. Let M be the event that the
participant brought a microwave and let C be the event that the
participant brought a video game console. Organize these events in a
two-way table. What is the probability that the participant brought a
microwave or a console, P(M or C)? Answer: C. 0.90
◉ According to sales records at a local coffee shop, 75% of all
customers like hot coffee, 30% like iced coffee, and 22% like both
hot and iced coffee. The Venn diagram displays the coffee
preferences of the customers.
A randomly selected customer is asked if they like hot or iced coffee.
Let H be the event that the customer likes hot coffee and let I be the
event that the customer likes iced coffee. What is the probability that
