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14 Jan 2021, 05:00
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C
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Difficulty:
55%
(hard)
Question Stats:
58% (01:59) correct
42%
(02:06)
wrong
based on 191
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Not Attempted Yet
Ms Li works at an office where the work timing is from 9:00 AM to 6:00 PM. 25% of a year she goes late to office and 35% of a year she leaves early from office. If P is the probability that she works at office the entire working day then
A. 0.25 ≤ P ≤ 0.35
B. 0.25 ≤ P ≤ 0.65
C. 0.4 ≤ P ≤ 0.65
D. 0.35 ≤ P ≤ 0.4
E. 0.1 ≤ P ≤ 0.6
A. 0.25 ≤ P ≤ 0.35
B. 0.25 ≤ P ≤ 0.65
C. 0.4 ≤ P ≤ 0.65
D. 0.35 ≤ P ≤ 0.4
E. 0.1 ≤ P ≤ 0.6
17 Jan 2021, 08:45
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Good morning Bunuel,
Here is what I think. Mr. Li either late in the morning or early leaving in the afternoon or both. P is the percentage of working entire day, which no late or no leaving early or both. P should be 1-(25%+35%-L&E%). > or = 45%.
Only answer C 0.4<=P<=0.65 is in the range. Therefore, I think the answer is C.
Please comment.
Thank you.
Posted from my mobile device
Here is what I think. Mr. Li either late in the morning or early leaving in the afternoon or both. P is the percentage of working entire day, which no late or no leaving early or both. P should be 1-(25%+35%-L&E%). > or = 45%.
Only answer C 0.4<=P<=0.65 is in the range. Therefore, I think the answer is C.
Please comment.
Thank you.
Posted from my mobile device
18 Jan 2021, 10:00
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Let's L be the event of being late and E be the event of being early then we have:
P(L) = 0.25 and P(E) = 0.35
Now the question is basically asking for the probability of the event "not being late AND not being early" so we have:
P(not L) = 0.75 and P(not E) = 0.65
We know that the maximum value of P(A and B) is the lower of the two probabilities, P(A) and P(B) so the maximum of P(not L & not E) = 0.65
We also know that P(A or B) can not exceed 1 so P(not L OR not E) can not exceed 1 and we have:
P(not L OR not E) = P(not L) + P(not E) - P(not L AND not E)
1 = 0.75 + 0.65 - P(not L AND not E)
1 = 1.40 - P(not L AND not E) => P(not L AND not E) should be at least 0.40
Answer is C.
P(L) = 0.25 and P(E) = 0.35
Now the question is basically asking for the probability of the event "not being late AND not being early" so we have:
P(not L) = 0.75 and P(not E) = 0.65
We know that the maximum value of P(A and B) is the lower of the two probabilities, P(A) and P(B) so the maximum of P(not L & not E) = 0.65
We also know that P(A or B) can not exceed 1 so P(not L OR not E) can not exceed 1 and we have:
P(not L OR not E) = P(not L) + P(not E) - P(not L AND not E)
1 = 0.75 + 0.65 - P(not L AND not E)
1 = 1.40 - P(not L AND not E) => P(not L AND not E) should be at least 0.40
Answer is C.
