In: Statistics and Probability
The management of a business concern will be making a decision whether to upgrade their office desktops to Windows 10 from Windows 7. However the management wants to see whether the employees are feeling comfortable in using Windows 10. A one-day training was organized on Windows 10, where all the personnel participated, of whom 16% are secretaries (A). After the seminar a survey was taken. It shows that among secretaries 53% want upgrade to Windows 10 (W10), 16% want no change from Windows 7 (W7), 31% have no preference (NP). Among non-secretarial employees the respective percentages are 35%, 52% and 13%.
As it has been mentioned above that 16% of secretaries want no
change from Windows 7. Which of the following is the correct
representation of that fact?
P(W7 ∩ A) = 0.16
P(A | W7) = 0.16
P(W7 | A) = 0.16
None of the above
Tries 0/3 |
If a personnel is selected at random, what is the probability that she made a definite preference, given that she is not a secretary?
Tries 0/5 |
If a personnel is selected at random, what is the probability that she made a definite preference? Answer to 3 digits after decimal.
Tries 0/5 |
If a personnel is selected at random, what is the probability that she is not a secretary, given that she made a definite preference? Answer to 3 digits after decimal.
A: Event of a randomly selected personnel is a secretary
P(A) = 16/100=0.16
: Event of a randomly selected personnel is not a secretary
P() =1-P(A) = 0.84
It shows that among secretaries 53% want upgrade to Windows 10 (W10), 16% want no change from Windows 7 (W7), 31% have no preference (NP)
i.e
P(W10|A) = Probability that the person wanted upgrade to Windows 10 given that the person is a secretary = 0.53
P(W7|A) = Probability that the person wanted no change given that the person is a secretary = 0.16
P(NP|A) = Probability that the person has no preference given that the person is a secretary = 0.31
Among non-secretarial employees the respective percentages are 35%, 52% and 13%.
P(W10|) = 0.35
P(W7|) = 0.52
P(NP|) = 0.13
As it has been mentioned above that 16% of secretaries want no
change from Windows 7. Which of the following is the correct
representation of that fact?
Answer : P(W7 | A) = 0.16
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If a personnel is selected at random, probability that she has no preference, given that she is not a secretary
= P(NP|)=0.13
P : event of person made a definite
preference
If a personnel is selected at random, probability that she made a
definite preference, given that she is not a secretary =
P(P|)
= 1-P(NP|)
= 1-0.13 = 0.87
If a personnel is selected at random, probability that she made a definite preference, given that she is not a secretary =0.87
Answer : 0.87
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If a personnel is selected at random, the probability that she made a definite preference = P(P)
P(A) = 0.16
P() = 0.84
P(NP|A) = 0.31
P(P|A) = 1 - P(NP|A) =1-0.31=0.69
P(P|) = 1-P(NP|) = 1-0.13 = 0.87
P(P|A) : If a personnel is selected at random, probability that she made a definite preference, given that she is a secretary =0.69
Event of person made a definite preference = Event that the randomly selected person is secretary and made a definite preference OR Event that the randomly selected person is not secretary and made a definite preference
i.e
P(P) = P(A)P(P|A) + P()P(P|) = 0.16 x 0.69 + 0.84 x 0.87 = 0.1104+0.7308 = 0.8412
If a personnel is selected at random, the probability that she made a definite preference = 0.8412
Answer : 0.841
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If a personnel is selected at random, probability that she is not a secretary, given that she made a definite preference
= P(|P)
By Bayes theroem,
P()P(P|) = 0.84 x 0.87 = 0.7308
P(A)P(P|A) + P()P(P|) = 0.16 x 0.69 + 0.84 x 0.87 = 0.1104+0.7308 = 0.8412
If a personnel is selected at random, probability that she is not a secretary, given that she made a definite preference = 0.869
Answer : 0.869