Download Ch 14 and 15 Probability Review with Vocabulary

Ch 13-14 Probability Review with Vocabulary
Sample space:
Event:
Outcome:
Complement rule:
1.
What is the sample space when a fair die is rolled? Are the outcomes equally likely?
2.
An experiment consists of tossing a dice and then flipping a coin once if the number on the dice is even or flipping a coin twice if
the number on the dice is odd. What it the sample space?
3.
Roll a dice twice. Observe the numbers landed on. What is the probability of observing:
a) two 5’s?
b) observing at least one 5?
General Addition rule:
Conditional probability:
-if the events are disjoint then the Addition rule is:
Mutually exclusive:
General Multiplication rule:
Independence:
c) exactly one 5?
-if the events are independent then the Multiplication rule is:
4.
Records show that 20% of Clements students are seniors. They also show that 35% of all Clements students play sports and that
13% of the seniors play sports (probability of sports given senior = .13). Answer the following:
a) If a student is chosen at random, what is the probability that they will be a senior or play sports?
b) Given that a student is a senior, what is the probability that they play sports?
c)
Given that a student plays sports, what is the probability that they are a senior?
d) Are the events being a senior and playing sports independent? Explain.
5.
A high school senior applies to college A and B. He estimates that the probability of being admitted to A is .7, the probability
that his application will be rejected at B is .5 and that the probability that at least one of his applications being rejected is .6. What
is the probability that he will be admitted to at least one of the colleges?
6.
Mr. Garcia’s 1st period class has 25 students. Five are in band. Eighteen have A’s. Six are neither in band nor have A’s. If a band
student from his class is selected, what is the probability that they have an A?
7.
In Hitense City, 35% of adults have high blood pressure or high cholesterol. One out of every four people has high blood
pressure, and one out of every five has high cholesterol. Find the probability that a person chosen at random will have both high
blood pressure and high cholesterol.
8.
Complete this table so that the events survived and male are independent.
Male
Female
Survived
Total
650
Did Not Survive
Total
9.
1640
2000
Suppose that 3% of a clinic’s patients are known to have a certain disease. A test is developed that is positive in 99% of patients
with the disease, but it is also positive in 5% of patients who do not have the disease. A patient is chosen at random from the
clinic. What is the probability that the person actually has the disease given that the test comes out positive?
10. Suppose that among all U.S. adults, 60% are married and 55% have college degrees. And 20% are neither married nor have a
college degree. If you select an adult at random, what is the probability that the adult has a college degree but he/she is not
married?
11. Multiple Choice:
a) If events A and B are independent and P(A) = 0.3 and P(B) = 0.5, then which of these is true? Circle the correct one.
A. P(A and B) = 0.8
B. P(A or B) = 0.15
C. P(A or B) = 0.8
D. P(A | B) = 0.3
E. P(A | B) = 0.5
C. P(A | B)
D. P(A) + P(B)
E. P(B) · P(A | B)
b) For all events A and B, P(A and B) =
A. P(A) · P(B)
B.P(B | A)
12. True or False:
a) Two events, each with probability greater than 0, are mutually exclusive (disjoint). The probability that both occur on the same
opportunity is 0.
b) Suppose you flip a fair coin and get five heads in a row. The probability that you will get a tail on the next flip is less than 0.5
c) If P(A) = .2 and P(B) = .5 and A and B are independent, then P(A or B) = .7
d) If P(A) = .2 and P(B) = .5 and A and B are mutually exclusive, is P(A  B) = 0
13. The sale bin in a clothing store contains an assortment of t-shirts in different sizes. There are 7 small, 8 medium, and 4 large
shirts. Alan is looking for a large shirt. He starts grabbing shirts one at a time and checking the size. After he checks each shirt, he
leaves it outside the bin. Show your work!
a) What is the probability that at least one of the first four shirts he checks is a large?
b) What is the probability that the first large shirt he finds is the third one he checks?
14. In the ABC Health Club, the probability that a member picked at random is a doctor is .4, the probability that the member is a
male is 0.5, and the probability that the member is a male given that he is a doctor is 0.6. Find the probability that the member is
a doctor or a male.
15. Suppose 80% of the homes in Katy have a desktop computer, 70% have a laptop computer, and 30% have both a desktop
computer and a laptop computer. What is the probability that a randomly selected home will have a laptop computer given that
they have a desktop computer?
16. Due to turnover and absenteeism at an assembly plant, 20% of the items are assembled by inexperienced employees.
Management has determined that customers return 12% of the items assembled by inexperienced employees, whereas only 3% of
the items assembled by experienced employees are returned. If an item is returned, what is the probability that it was assembled
by an inexperienced employee? (Hint: use a tree diagram)
17. A UT band member is required to wear a plain white T-shirt under their uniform. According to Clements’s records, about 15% of
the band will forget each game. If the director checks five band members at random, what is the probability that at least one of
them will be wearing the required T-shirt?
18. Check of dorm rooms on a large college campus revealed that 38% had refrigerators, 52% had TV’s, and 21% had both a TV and
a fridge. What’s the probability that a randomly selected dorm room has:
a) a TV but not a fridge? _________
b) a TV or a fridge but not both? _________
c) neither a TV nor a fridge? _________
19. A company’s records indicate that on any given day about 1% of their day shift employees and 2% of their night shifts employees
will miss work. 60% of the employees work the day shift.
a What percent of the absent employees are on the night shift?
b. Is absenteeism independent of shift worked? Explain.
20. In an experiment to study the relationship of hypertension and smoking habits, the following data are collected from 180
individuals.
Non-smokers Moderate smokers Heavy smokers
Hypertension
21
36
30
No hypertension
48
26
19
a) What is the probability that a person selected has hypertension?
b) What is the probability that a person selected has hypertension and is a heavy smoker?
c) What is the probability that a person selected has hypertension given they are a heavy smoker?
d) What is the probability that a person selected has hypertension or is a heavy smoker?
e)
Is being a non-smoker and not having hypertension independent?