A fair coin is tossed three times, and the events A and B are defined as shown below. Complete parts a through d. A: {At most one head is observed} B: {The number of heads
A fair coin is tossed three times, and the events A and B are defined as shown below. Complete parts a through d. A: {At most one head is observed} B: {The number of heads
Algebra and Trigonometry (MindTap Course List)
4th Edition
ISBN:9781305071742
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter14: Counting And Probability
Section14.2: Probability
Problem 4E: Let E and F be events in a sample space S. aThe probability of E and F occurring is...
Related questions
Question
A fair coin is tossed
three
times, and the events A and B are defined as shown below. Complete parts a through
d.
A: {At
most
one
head
is observed}B: {The number of
heads
observed is
even}
a. Identify the sample points in the events A, B,
A∪B,
Ac,
and
A∩B.
Identify the sample points in the event A. Choose the correct answer below.
A:{HHH, THH, HTH, HHT}
A:{TTT, HTT, THT, TTH}
A:{HHT, HTH, THH, TTT}
There are no sample points in the event.
Identify the sample points in the event B. Choose the correct answer below.
B:{TTT, HTT, THT, TTH}
B:{HHT, HTH, THH, TTT}
B:{HHH, THH, HTH, HHT}
Identify the sample points in the event
A∪B.
Choose the correct answer below.A∪B:{HHH, THH, HTH, HHT}
A∪B:{HHT, HTH, THH, TTT}
A∪B:{TTT, HTT, THT, TTH, THH, HTH, HHT}
There are no sample points in the event.
Identify the sample points in the event
Ac.
Choose the correct answer below.Ac:{TTT, HTT, THT, TTH}
Ac:{TTT}
Ac:{HHH, THH, HTH, HHT}
There are no sample points in the event.
Identify the sample points in the event
A∩B.
Choose the correct answer below.A∩B:{TTT, HTT, THT, TTH}
A∩B:{HHH, THH, HTH, HHT}
A∩B: {TTT}
There are no sample points in the event.
b. Find P(A), P(B),
P(A∪B),
PAc,
and
P(A∩B)
by summing the probabilities of the appropriate sample points.P(A)=enter your response here
(Type an integer or simplified fraction.)Find P(B).
P(B)=enter your response here
(Type an integer or simplified fraction.)Find
P(A∪B).
P(A∪B)=enter your response here
(Type an integer or simplified fraction.)Find
PAc.
PAc=enter your response here
(Type an integer or simplified fraction.)Find
P(A∩B).
P(A∩B)=enter your response here
(Type an integer or simplified fraction.)c. Find
additive rule . Compare your answer to the one you obtained in part
P(A∪B)
using the b.
P(A∪B)=enter your response here
(Type an integer or simplified fraction.)Compare your answer to the one you obtained in part
b.
Choose the correct answer below.The value of
P(A∪B)
calculated using the additive rule is less than
P(A∪B)
calculated by summing the probabilities of the sample points.Both calculations of
P(A∪B)
produce the same result.P(A∪B)
calculated using the additive rule is greater than
P(A∪B)
calculated by summing the probabilities of the sample points.d. Are events A and B mutually exclusive? Why?
No,
events A and B
are not
mutually exclusive because
P(A∩B)≠0.
Yes,
events A and B
are
mutually exclusive because
P(A∩B)≠0.
Yes,
events A and B
are
mutually exclusive because
P(A∩B)=0.
No,
events A and B
are not
mutually exclusive because
P(A∩B)=0
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