Three people each flip a fair coin. Define the following events: A: exactly three heads are observed B: at least two tails are observed Use this information to answer the following questions. Please round all answers to three decimals if necessary (you may also leave your answers as fractions) (a) How many elements are in the sample space? n(S) = (enter an integer) (b) Compute P(A) = (enter your answer to four decimals) (c) Compute P(B) = (enter your answer to four decimals) (d) Compute P(A or B) = (enter your answer to four decimals) (e) Compute P(A And not B) (enter your answer to four decimals) (f) Are events A and B mutually exclusive? Select the most appropriate response below. A. A and B are mutually exclusive events because P(A And B) = 0. B. A and B are not mutually exclusive events because P(A And B) = 0. C. A and B are mutually exclusive events because P(A or B) = 0. D. A and B are not mutually exclusive events because P(A and B) + 0. E. A and B are not mutually exclusive events because P(A Or B) ± 0. F. A and B are mutually exclusive events because P(A And B) ± 0.
Three people each flip a fair coin. Define the following events: A: exactly three heads are observed B: at least two tails are observed Use this information to answer the following questions. Please round all answers to three decimals if necessary (you may also leave your answers as fractions) (a) How many elements are in the sample space? n(S) = (enter an integer) (b) Compute P(A) = (enter your answer to four decimals) (c) Compute P(B) = (enter your answer to four decimals) (d) Compute P(A or B) = (enter your answer to four decimals) (e) Compute P(A And not B) (enter your answer to four decimals) (f) Are events A and B mutually exclusive? Select the most appropriate response below. A. A and B are mutually exclusive events because P(A And B) = 0. B. A and B are not mutually exclusive events because P(A And B) = 0. C. A and B are mutually exclusive events because P(A or B) = 0. D. A and B are not mutually exclusive events because P(A and B) + 0. E. A and B are not mutually exclusive events because P(A Or B) ± 0. F. A and B are mutually exclusive events because P(A And B) ± 0.
College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter8: Sequences, Series, And Probability
Section8.CT: Chapter Test
Problem 24CT: Show the sample space of the experiment: toss a fair coin three times.
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Transcribed Image Text:Three people each flip a fair coin. Define the following events:
A: exactly three heads are observed
B: at least two tails are observed
Use this information to answer the following questions. Please round all answers to three decimals if necessary (you may also leave your answers as
fractions)
(a) How many elements are in the sample space?
n(S) =
(enter an integer)
(b) Compute P(A) =
(enter your answer to four decimals)
(c) Compute P(B) =
(enter your answer to four decimals)
(d) Compute P(A or B) =
(enter your answer to four decimals)
(e) Compute P(A And not B)
(enter your answer to four decimals)
(f) Are events A and B mutually exclusive? Select the most appropriate response below.
A. A and B are mutually exclusive events because P(A And B) = 0.
B. A and B are not mutually exclusive events because P(A And B) = 0.
C. A and B are mutually exclusive events because P(A or B) = 0.
D. A and B are not mutually exclusive events because P(A and B) + 0.
E. A and B are not mutually exclusive events because P(A Or B) ± 0.
F. A and B are mutually exclusive events because P(A And B) ± 0.
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