Ms Li works at an office where the work timing is from 9:00 AM to 6:00

Question

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

Taikiqi · Answer

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

HamedATX · Answer

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.

unraveled · Answer

If Ms Li's late arrival probability does not overlaps with her early leaving probability then we are left with (0.25) + (0.35) + x = 1, where x is the probability(min.) of her working the entire day. 
 \implies x_{min} = 0.40     
If the two probabilities fully overlap then we have ((0.25) + 10) + x = 1, where now x is probability(max.) of her working the entire day. 
 \implies x_{max} = 0.65

Answer C.

ronaldoSuiiii · Answer

Can we do like this?

Not late= 0.75
Not leaving early= 0.65

Thus, full working day= not late percent of not leaving early i.e. 0.75*0.65 ( 75% of 65%)
= 0.4875 (48.75%)

Thus, option C.

Am I doing it right?

unraveled · Answer

ronaldoSuiiii 
Don't you think all the option fulfil the criteria you are applying. How only C is the answer??
P is some range which is what we need to establish. I guess you missed in that part.

Please check.

ronaldoSuiiii · Answer

CelestialBro · Answer

This feels a lot more like a maximizing set question than a probability question.
Say there were total 100 days
We can consider two scenarios here:
 case 1: where she is late P(L) and days when she leaves early P(E) are separate days ie. there is no overlap: 
P(E)+P(L)=35+25=60 days

so the remaining good days are 100-60= 40 perfect days.

case 2: when she is late and also left early on the same day: 
the 35 days when she came late is the max boundary here which also contains the 25 days when she also left early.
this leaves us with 65 perfect days.

So the perfect day range is 40<=P<=65  so option C

Ms Li works at an office where the work timing is from 9:00 AM to 6:00

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Ms Li works at an office where the work timing is from 9:00 AM to 6:00

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

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745 with Only Self-Prep and GMAT Club

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