A frustrated store manager is asked to make four different yes-no decisions that have no relation to each other. Because he is impatient to leave work, he flips a coin for each decision. Construct an equiprobable sample space for the sequence of four yes-no decisions. The number of elements in the sample space is n(S) = The number of elements in the sample space with all four yes decisions is n(E) = The number of elements in the sample space with all four no decisions is n(F) = The number of elements in the sample space with two yes and two no decisions is n(G) = If the correct decision in each case was yes, what is the probability that the following will occur? (Enter your probabilities as simplified fractions.) (a) All of his decisions were correct. n(E) n(S) Pr(E) = (b) None of his decisions were correct. n(F) n(S) Pr(F) = = Pr(G) = = (c) Half of his decisions were correct. n(G)
A frustrated store manager is asked to make four different yes-no decisions that have no relation to each other. Because he is impatient to leave work, he flips a coin for each decision. Construct an equiprobable sample space for the sequence of four yes-no decisions. The number of elements in the sample space is n(S) = The number of elements in the sample space with all four yes decisions is n(E) = The number of elements in the sample space with all four no decisions is n(F) = The number of elements in the sample space with two yes and two no decisions is n(G) = If the correct decision in each case was yes, what is the probability that the following will occur? (Enter your probabilities as simplified fractions.) (a) All of his decisions were correct. n(E) n(S) Pr(E) = (b) None of his decisions were correct. n(F) n(S) Pr(F) = = Pr(G) = = (c) Half of his decisions were correct. n(G)
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:A frustrated store manager is asked to make four different yes-no decisions that have no relation to each other. Because he is
impatient to leave work, he flips a coin for each decision.
Construct an equiprobable sample space for the sequence of four yes-no decisions.
The number of elements in the sample space is n(S)
The number of elements in the sample space with all four yes decisions is n(E)
Pr(E)
The number of elements in the sample space with all four no decisions is n(F)
The number of elements in the sample space with two yes and two no decisions is n(G) =
If the correct decision in each case was yes, what is the probability that the following will occur? (Enter your probabilities as
simplified fractions.)
(a) All of his decisions were correct.
n(E)
n(S)
=
(b) None of his decisions were correct.
Pr(F)
n(F)
n(S)
Pr(G)
=
(c) Half of his decisions were correct.
n(G)
=
=
=
=
=
=
Expert Solution
Step 1
Each of the four decisions is yes/no.
So, for each of the desisions, we have 2 options.
Hence, total number of possible desion-combinations = 24 = 16.
So, n(S) = 16.
Only element in the sample space with all four yes decisions = yyyy [y = yes]
So, number of elements in the sample space with all four yes-decisions, n(E) = 1.
Only element in the sample space with all four no decisions = nnnn [n = no]
So, number of elements in the sample space with all four no-decisions, n(F) = 1.
Elements in the sample space with all two yes and two no decisions are {yynn, ynyn, ynny, nyny, nyyn, nnyy}
So, number of elements in the sample space with all four yes-decisions, n(G) = 6.
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