Probability Test - Denton Independent School District

AP Statistics Probability Block Name:
In an AP Stats class, 57% of students eat breakfast in the morning and 80% of students floss their teeth. Forty-six percent of
students eat breakfast and also floss their teeth.
1. What is the probability that a student from this class eats
breakfast but does not floss their teeth?
2. What is the probability that a student from this class eats
breakfast or flosses their teeth?
3. Five juniors and four seniors have applied for two open student council positions. School administrators have decided to
pick the new members randomly. What is the probability the council positions become both juniors or both seniors?
4. You are playing Rock-Paper-Scissors with a friend, in the desert, next to a cactus. When you win you get to stick a cactus
needle into your friends arm. Assume nobody is cheating and you are playing a fair game. Your friend has 17 needles in
his/her arm and you only have 5 needles in yours. What does the “Law of Large Numbers” say about the this scenario?
5. According to the National Telecommunication and Information Administration, 56.5% of U.S. households owned a
computer in 2001. What is the probability that of three randomly selected U.S. households at least one owned a
computer in 2001?
6. According to the National Telecommunication and Information Administration, 50.5% of U.S. households had Internet
access in 2001. What is the probability that four randomly selected U.S. households all had Internet access in 2001?
A person has three quarters, two dimes, a nickel and four pennies in his pocket. This person reaches into his pocket and
randomly pulls out three coins, one at a time.
7. What is the probability that he has exactly 55 cents? 8. What is the probability that he has at least one quarter?
9. Insurance company records indicate that 12% of all teenage drivers have been ticketed for speeding and 9% for going
through a red light. If 4 % have been ticketed for both, what is the probability that a teenage driver has been issued a
ticket for speeding but not for running a red light?
10. Below are pairs of events. Circle the all the pairs of events which are most likely to be independent.
A) Being a senior; wearing red socks to class B) Registering to vote; being left handed
C) Having a car accident; having a learners permit D) Doing the Statistics homework; getting an A on this test
E) Having 3 inches of snow in the morning; getting to school on time

10. Below are pairs of events. Circle the all the pairs of events which are most likely to be disjoint.
A) Being a senior; Being a freshman B) Being male; Being left handed
C) Having a car accident; Being drunk D) Taking this Stat test today; Being absent today
E) Building a snowman in your yard; Living in the Sahara Desert
11. A poll of 120 Ithacans found that 30 had visited the Museum of the Earth and that 80 had been to Home Depot. Fifteen
of those polled had never been to either. Assuming that Home Depot and the Museum of the Earth are independent
events, what percent of those polled had been to both?
12. Six Republicans and four Democrats have applied for two open positions on a planning committee. Since all the
applicants are qualified to serve, the City Council decides to pick the two new members randomly. What is the
probability that both come from the same party?
13. Fifteen percent of sports fans have purchased a football ticket and a basketball ticket in the past year. Fifty-five
percent have purchased exactly one or the other. Thirty percent have purchased a football ticket. What percent have
purchased a basketball ticket?
23% of Americans are overweight. 72% of overweight Americans have high blood pressure. 28% of non-overweight
Americans have high blood pressure.
14. What % of Americans have high blood pressure? 15. Of those that have high blood pressure, what % are
overweight?
16. Pepsi is running a sales promotion in which 12% of all bottles have a “FREE” logo under the cap. What is the probability
that you find two free ones in a 6-pack?
17. A supermarket claims that their checkout scanners correctly price 99.8% of the items sold. If you have 60 items that
are to be scanned, what is the probability that at least one of them is scanned incorrectly?

You are up for your annual job performance review. You estimate there’s a 30% chance you’ll get a promotion, a 40%
chance of a raise, and a 20% chance of getting both a raise and a promotion.
Use this space to build a picture of the information:
19. If you get the promotion, what is the probability you get
a raise?
21. Do you think getting a raise and getting a promotion are
independent events? Explain. (Simply “Yes” or “No” will
not receive any credit.)
18. What is the probability that you get a raise or a
promotion?
20. What is the probability that you get neither a raise nor a
promotion?
22. Do you think getting a raise and getting a promotion are
disjoint? Explain. (Simply “Yes” or “No” will not receive
any credit.)
A particular class has 20 seniors and 10 juniors. Three of the seniors are male and four of the juniors are female.
Use this space to build some kind of picture:
24. Of the males, what % are seniors?
23. If one student were selected randomly, what is the
probability they are male?
25. Of the seniors, what % are males?
26. The probability of being a Jibber and a Jabber is 42%. The probability of being a Jibber is 52.5%. The probability of
being a Jabber is 80%. Are the probabilities of being a Jibber and/or Jabber independent events? Explain.

Peter, Paul and Mary are playing the card game “Go Hunting”. Below are the hands. (I am showing you the hands but the
players cannot see each others’ cards)
Mary Peter Paul
27. Mary gets to select 1 card from Peter. What is the
probability it will be a 2?
29. Assume the cards are as shown again. What is the
probability that Paul has exactly 1 seven in his hand?
31. One dark and stormy night while visiting your
grandmother’s house a bunch of poison-dart blowing
Ninja’s cut off your electricity and stick you in the neck
with a poison dart. You only have three minutes to go to
the medicine cabinet and find the anti-poison-dart pills.
You find out that your grandmother stores all her pill in
one bottle to save space! Oh no!! It’s dark and you can’t
tell the pills apart. The bottle contains 6 Tylenol, 4
Ibuprofen and 4 anti-poison-dart pills. You only have
enough time left to swallow 3 pills. What is the
probability you will not die?
Administer
? ?
28. Assume the cards are as shown again. Paul gets to
select 2 cards from Mary. What is the probability
exactly one of them is a 5?
30. Assume the cards are as shown again. What is the
probability that Paul has at least 1 queen in his hand?
32. You go hiking in Colorado and bring along a 6-chamber
.44 magnum pistol in case you meet up with a maneating
bear. Before you left you forgot to buy bullets so
you put your only remaining bullet in the chamber and
spun the chamber like John Wayne. You didn’t bother
looking to see where the bullet ended up. Along the
trail you noticed a Ranger guide that alerted you that if
you shoot a man-eating bear with a .44 magnum pistol
you only have a 30% chance of killing it.
Oh no!! You have stumbled upon a man-eating bear
and it is charging at you at full speed. You only have
time to shoot 4 times. What is the probability you will
not die?
?
?