7:23 1 SECTION 5.2 Some Probability I 1 of 6 Done 219 SECTION 5.2 Some Probability Rules-Compound Events VIEWPOINT The Psychology of Odors The Smell and Taste Treatment Research Foundation of Chicago collected data on the time required to complete a maze while subjects were smelling different scents. Data for this survey can be fournd by visiting the web site for the Carnegie Mellon University Data and Story Library (DASL). Once at the DASL site, select Data Subjects, then Psychology, and then Scents. You can estimate conditional probabilities regarding response times for smokers, nonsmokers, and types of scents. SECTION 5.2 PROBLEMS 1.| Statistical Literacy If two events are mutually exclusive, can they occur concurrently? Explain. 2. Statistical Literacy If two events A and B are independent and you know that P(A) = 0.3, what is the value of P(A| B)? hssqe 3. | Basic Computation: Addition Rule Given P(A) = 0.3 and P(B) = 0.4: (a) If A and B are mutually exclusive events, compute P(A or B). (b) If P(A and B) = 0.1, compute P(A or B). 4. | Basic Computation: Addition Rule Given P(A) = 0.7 and P(B) = 0.4: (a) Can events A and B be mutually exclusive? Explain. (b) If P(A and B) = 0.2, compute P(A or B). buta ollos l 5. | Basic Computation: Multiplication Rule Given P(A) (a) If A and B are independent events, compute P(A and B). (b) If P(A | B) = 0.1, compute P(A and B). = 0.2 and P(B) = 0.4: 6. | Basic Computation: Multiplication Rule Given P(A) = 0.7 and P(B) = 0.8: (a) If A and B, are independent events, compute P(A and B). (b) If P(B|A) = 0.9, compute P(A and B). 7. | Basic Computations: Rules of Probability Given P(A) = 0.2, P(B) = 0.5, P(A | B) = 0.3: (a) Compute P(A and B). (b) Compute P(A or B). 8. | Basic Computation: Rules of Probability Given P(A°) = 0.8, P(B) = 0.3, P(B|A) = 0.2: (a) Compute P(A and B). (b) Compute P(A or B). uls Critical Thinking Lisa is making up questions for a small quiz on prob- ability. She assigns these probabilities: P(A) = 0.3, P(B) = 0.3, P(A and B) = 0.4. What is wrong with these probability assignments? 9. 10. | Critical Thinking Greg made up another question for a small quiz. He as- signs the probabilities P(A) = 0.6, P(B) = 0.7, P(A | B) = 0.1 and asks for the probability P(A or B). What is wrong with the probability assignments? 11. | Critical Thinking Suppose two events A and B are mutually exclusive, with P(A) # 0 and P(B) # 0. By working through the following steps, you'll see why two mutually exclusive events are not independent. (a) For mutually exclusive events, can event A occur if event B has occurred? What is the value of P(A | B)? (b) Using the information from part (a), can you conclude that events A and B are not independent if they are mutually exclusive? Explain. ETITI 7:23 1 SECTION 5.2 Some Probability I Done 2 of 6 220 Chapter 5 ELEMENTARY PROBABILITY THEORY independent, with P(A) # 0 and P(B) + 0. By working through the following steps, you'll see 12. Critical Thinking Suppose two events A and B are why two independent events are not mutually exclusive. (a) What formula is used to compute P(A and B)? Is P(A and B) o Explain. (b) Using the information from part (a), can you conclude that events A and B are not mutually exclusive? 13. | Critical Thịnking Consider the following events for a driver selected at random from the general population: A = driver is under 25 years old B = driver has received a speeding ticket Translate each of the following phrases into symbols. (a) The probability the driver has received a speeding ticket and is under 25 years old (b) The probability a driver who is under 25 years old has received a spea u ing ticket (c) The probability a driver who has received a speeding ticket is 25 old or older years (d) The probability the driver is under 25 years old or has received a ticket speeding (e) The probability the driver has not received a speeding ticket or is under 25 years old 14. | Critical Thinking Consider the following events for a college student selected at random: A = student is female B = student is majoring in business Translate each of the following phrases into symbols. (a) The probability the student is male or is majoring in business (b) The probability a female student is majoring in business (c) The probability a business major is female (d) The probability the student is female and is not majoring in business (e) The probability the student is female and is majoring in business 15. | General: Candy Colors M&M plain candies come in various colors. The distribution of colors for plain M&M candies in a custon bag is Color Purple Yellow Red Orange Greer: Blue Brown Percentage 20% 20% 20% 10% 10% 10% 10% Suppose you have a large custom bag of plain M&M candies and one candy at random. Find (a) P(green candy or blue candy). Are these outcomes mutually exclusive? Why? (b) P(yellow candy or red candy). Are these outcomes mutually exclusive? Why? (c) P(not purple candy) you choose 16. | Environmental: Land Formations Arches National Park is located in southern Utah. The park is famous for its beautiful desert landscape and its many natural sandstone arches. Park Ranger Edward McCarrick started an inventory (not yet complete) of natural arches within the park that have an opening of at least 3 feet. The following table is based on information taken
7:23 1 SECTION 5.2 Some Probability I 1 of 6 Done 219 SECTION 5.2 Some Probability Rules-Compound Events VIEWPOINT The Psychology of Odors The Smell and Taste Treatment Research Foundation of Chicago collected data on the time required to complete a maze while subjects were smelling different scents. Data for this survey can be fournd by visiting the web site for the Carnegie Mellon University Data and Story Library (DASL). Once at the DASL site, select Data Subjects, then Psychology, and then Scents. You can estimate conditional probabilities regarding response times for smokers, nonsmokers, and types of scents. SECTION 5.2 PROBLEMS 1.| Statistical Literacy If two events are mutually exclusive, can they occur concurrently? Explain. 2. Statistical Literacy If two events A and B are independent and you know that P(A) = 0.3, what is the value of P(A| B)? hssqe 3. | Basic Computation: Addition Rule Given P(A) = 0.3 and P(B) = 0.4: (a) If A and B are mutually exclusive events, compute P(A or B). (b) If P(A and B) = 0.1, compute P(A or B). 4. | Basic Computation: Addition Rule Given P(A) = 0.7 and P(B) = 0.4: (a) Can events A and B be mutually exclusive? Explain. (b) If P(A and B) = 0.2, compute P(A or B). buta ollos l 5. | Basic Computation: Multiplication Rule Given P(A) (a) If A and B are independent events, compute P(A and B). (b) If P(A | B) = 0.1, compute P(A and B). = 0.2 and P(B) = 0.4: 6. | Basic Computation: Multiplication Rule Given P(A) = 0.7 and P(B) = 0.8: (a) If A and B, are independent events, compute P(A and B). (b) If P(B|A) = 0.9, compute P(A and B). 7. | Basic Computations: Rules of Probability Given P(A) = 0.2, P(B) = 0.5, P(A | B) = 0.3: (a) Compute P(A and B). (b) Compute P(A or B). 8. | Basic Computation: Rules of Probability Given P(A°) = 0.8, P(B) = 0.3, P(B|A) = 0.2: (a) Compute P(A and B). (b) Compute P(A or B). uls Critical Thinking Lisa is making up questions for a small quiz on prob- ability. She assigns these probabilities: P(A) = 0.3, P(B) = 0.3, P(A and B) = 0.4. What is wrong with these probability assignments? 9. 10. | Critical Thinking Greg made up another question for a small quiz. He as- signs the probabilities P(A) = 0.6, P(B) = 0.7, P(A | B) = 0.1 and asks for the probability P(A or B). What is wrong with the probability assignments? 11. | Critical Thinking Suppose two events A and B are mutually exclusive, with P(A) # 0 and P(B) # 0. By working through the following steps, you'll see why two mutually exclusive events are not independent. (a) For mutually exclusive events, can event A occur if event B has occurred? What is the value of P(A | B)? (b) Using the information from part (a), can you conclude that events A and B are not independent if they are mutually exclusive? Explain. ETITI 7:23 1 SECTION 5.2 Some Probability I Done 2 of 6 220 Chapter 5 ELEMENTARY PROBABILITY THEORY independent, with P(A) # 0 and P(B) + 0. By working through the following steps, you'll see 12. Critical Thinking Suppose two events A and B are why two independent events are not mutually exclusive. (a) What formula is used to compute P(A and B)? Is P(A and B) o Explain. (b) Using the information from part (a), can you conclude that events A and B are not mutually exclusive? 13. | Critical Thịnking Consider the following events for a driver selected at random from the general population: A = driver is under 25 years old B = driver has received a speeding ticket Translate each of the following phrases into symbols. (a) The probability the driver has received a speeding ticket and is under 25 years old (b) The probability a driver who is under 25 years old has received a spea u ing ticket (c) The probability a driver who has received a speeding ticket is 25 old or older years (d) The probability the driver is under 25 years old or has received a ticket speeding (e) The probability the driver has not received a speeding ticket or is under 25 years old 14. | Critical Thinking Consider the following events for a college student selected at random: A = student is female B = student is majoring in business Translate each of the following phrases into symbols. (a) The probability the student is male or is majoring in business (b) The probability a female student is majoring in business (c) The probability a business major is female (d) The probability the student is female and is not majoring in business (e) The probability the student is female and is majoring in business 15. | General: Candy Colors M&M plain candies come in various colors. The distribution of colors for plain M&M candies in a custon bag is Color Purple Yellow Red Orange Greer: Blue Brown Percentage 20% 20% 20% 10% 10% 10% 10% Suppose you have a large custom bag of plain M&M candies and one candy at random. Find (a) P(green candy or blue candy). Are these outcomes mutually exclusive? Why? (b) P(yellow candy or red candy). Are these outcomes mutually exclusive? Why? (c) P(not purple candy) you choose 16. | Environmental: Land Formations Arches National Park is located in southern Utah. The park is famous for its beautiful desert landscape and its many natural sandstone arches. Park Ranger Edward McCarrick started an inventory (not yet complete) of natural arches within the park that have an opening of at least 3 feet. The following table is based on information taken
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ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
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Transcribed Image Text:7:23 1
SECTION 5.2 Some Probability I
1 of 6
Done
219
SECTION 5.2 Some Probability Rules-Compound Events
VIEWPOINT The Psychology of Odors
The Smell and Taste Treatment Research Foundation of Chicago collected data on the time required
to complete a maze while subjects were smelling different scents. Data for this survey can be fournd
by visiting the web site for the Carnegie Mellon University Data and Story Library (DASL). Once at
the DASL site, select Data Subjects, then Psychology, and then Scents. You can estimate conditional
probabilities regarding response times for smokers, nonsmokers, and types of scents.
SECTION 5.2 PROBLEMS
1.| Statistical Literacy If two events are mutually exclusive, can they occur
concurrently? Explain.
2. Statistical Literacy If two events A and B are independent and you know
that P(A) = 0.3, what is the value of P(A| B)?
hssqe
3. | Basic Computation: Addition Rule Given P(A) = 0.3 and P(B) = 0.4:
(a) If A and B are mutually exclusive events, compute P(A or B).
(b) If P(A and B) = 0.1, compute P(A or B).
4. | Basic Computation: Addition Rule Given P(A) = 0.7 and P(B) = 0.4:
(a) Can events A and B be mutually exclusive? Explain.
(b) If P(A and B) = 0.2, compute P(A or B).
buta ollos l
5. | Basic Computation: Multiplication Rule Given P(A)
(a) If A and B are independent events, compute P(A and B).
(b) If P(A | B) = 0.1, compute P(A and B).
= 0.2 and P(B) = 0.4:
6. | Basic Computation: Multiplication Rule Given P(A) = 0.7 and P(B) = 0.8:
(a) If A and B, are independent events, compute P(A and B).
(b) If P(B|A) = 0.9, compute P(A and B).
7. | Basic Computations: Rules of Probability Given P(A) = 0.2, P(B) = 0.5,
P(A | B) = 0.3:
(a) Compute P(A and B).
(b) Compute P(A or B).
8. | Basic Computation: Rules of Probability Given P(A°) = 0.8, P(B) = 0.3,
P(B|A) = 0.2:
(a) Compute P(A and B).
(b) Compute P(A or B).
uls
Critical Thinking Lisa is making up questions for a small quiz on prob-
ability. She assigns these probabilities: P(A) = 0.3, P(B) = 0.3, P(A and B) =
0.4. What is wrong with these probability assignments?
9.
10. | Critical Thinking Greg made up another question for a small quiz. He as-
signs the probabilities P(A) = 0.6, P(B) = 0.7, P(A | B) = 0.1 and asks for
the probability P(A or B). What is wrong with the probability assignments?
11. | Critical Thinking Suppose two events A and B are mutually exclusive, with
P(A) # 0 and P(B) # 0. By working through the following steps, you'll see
why two mutually exclusive events are not independent.
(a) For mutually exclusive events, can event A occur if event B has occurred?
What is the value of P(A | B)?
(b) Using the information from part (a), can you conclude that events A and
B are not independent if they are mutually exclusive? Explain.
ETITI
Transcribed Image Text:7:23 1
SECTION 5.2 Some Probability I
Done
2 of 6
220
Chapter 5 ELEMENTARY PROBABILITY THEORY
independent, with
P(A) # 0 and P(B) + 0. By working through the following steps, you'll see
12. Critical Thinking Suppose two events A and B are
why two independent events are not mutually exclusive.
(a) What formula is used to compute P(A and B)? Is P(A and B) o
Explain.
(b) Using the information from part (a), can you conclude that events A and
B are not mutually exclusive?
13. | Critical Thịnking Consider the following events for a driver selected at
random from the general population:
A = driver is under 25 years old
B = driver has received a speeding ticket
Translate each of the following phrases into symbols.
(a) The probability the driver has received a speeding ticket and is under
25 years old
(b) The probability a driver who is under 25 years old has received a spea u
ing ticket
(c) The probability a driver who has received a speeding ticket is 25
old or older
years
(d) The probability the driver is under 25 years old or has received a
ticket
speeding
(e) The probability the driver has not received a speeding ticket or is under
25 years old
14. | Critical Thinking Consider the following events for a college student
selected at random:
A = student is female
B = student is majoring in business
Translate each of the following phrases into symbols.
(a) The probability the student is male or is majoring in business
(b) The probability a female student is majoring in business
(c) The probability a business major is female
(d) The probability the student is female and is not majoring in business
(e) The probability the student is female and is majoring in business
15. | General: Candy Colors M&M plain candies come in various colors. The
distribution of colors for plain M&M candies in a custon bag is
Color
Purple
Yellow
Red
Orange
Greer:
Blue
Brown
Percentage
20%
20%
20%
10%
10%
10%
10%
Suppose you have a large custom bag of plain M&M candies and
one candy at random. Find
(a) P(green candy or blue candy). Are these outcomes mutually exclusive?
Why?
(b) P(yellow candy or red candy). Are these outcomes mutually exclusive?
Why?
(c) P(not purple candy)
you
choose
16. | Environmental: Land Formations Arches National Park is located in
southern Utah. The park is famous for its beautiful desert landscape and its
many natural sandstone arches. Park Ranger Edward McCarrick started an
inventory (not yet complete) of natural arches within the park that have an
opening of at least 3 feet. The following table is based on information taken
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