Question

In: Statistics and Probability

The management of a business concern will be making a decision whether to upgrade their office...

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.

Solutions

Expert Solution

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

---------------------------------------------------------------

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


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