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# A bus stop is served by express buses, which run every hour at ten min

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Manager
Joined: 20 Dec 2004
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A bus stop is served by express buses, which run every hour at ten min  [#permalink]

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27 Jan 2008, 19:35
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(N/A)

Question Stats:

26% (01:28) correct 74% (03:06) wrong based on 18 sessions

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A bus stop is served by express buses, which run every hour at ten minutes past the hour, and local buses, which run every quarter of an hour, starting at five past the hour. What is the probability that a passenger arriving at the stop at random will have to wait more than six minutes for a bus?

(A) 1/2
(B) 31/60
(C) 29/60
(D) 1/15
(E) 11/20

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Re: A bus stop is served by express buses, which run every hour at ten min  [#permalink]

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27 Jan 2008, 21:56
10
3
$$p=\frac{9+9+9+4}{60}=\frac{31}{60}$$
Attachments

t59157.gif [ 15.48 KiB | Viewed 4370 times ]

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Director
Joined: 03 Sep 2006
Posts: 630
Re: A bus stop is served by express buses, which run every hour at ten min  [#permalink]

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27 Jan 2008, 21:47
neelesh wrote:
A bus stop is served by express buses, which run every hour at ten minutes past the hour, and local buses, which run every quarter of an hour, starting at five past the hour. What is the probability that a passenger arriving at the stop at random will have to wait more than six minutes for a bus?

I do have the OA but not sure how to arrive at that and hence looking for an explanation.

P = (4/60) + ( 4/60) + ( 9/60) + ( 9/60) + (10/60) = 36/60 = 3/5
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Bus Probability.PNG [ 19.92 KiB | Viewed 4373 times ]

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Re: A bus stop is served by express buses, which run every hour at ten min  [#permalink]

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27 Jan 2008, 22:07
walker wrote:
$$p=\frac{9+9+9+4}{60}=\frac{31}{60}$$

I am in the dark of this picture! I have the same start point, but do not know how to make the likelihood of it! help!
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Re: A bus stop is served by express buses, which run every hour at ten min  [#permalink]

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27 Jan 2008, 22:30
walker wrote:
$$p=\frac{9+9+9+4}{60}=\frac{31}{60}$$

Thanks walker, mistake in my case is that the last slot of 10 minutes is not needed which I have taken in my calculations.

If I remove that then it would be same and if I add that, then I am moving to the next hor slot!
Manager
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Re: A bus stop is served by express buses, which run every hour at ten min  [#permalink]

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27 Jan 2008, 23:19
Excellent explanation Walker.

Does this seem like a 2-minute type question ?
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Re: A bus stop is served by express buses, which run every hour at ten min  [#permalink]

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27 Jan 2008, 23:26
neelesh wrote:
Does this seem like a 2-minute type question ?

I guess yes. But I spent more than 15 min to draw it in PhotoShop....
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Re: A bus stop is served by express buses, which run every hour at ten min  [#permalink]

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28 Jan 2008, 13:32
neelesh wrote:
Excellent explanation Walker.

Does this seem like a 2-minute type question ?

i did a number line (made sure I take into account the last block properly).

btw, nice photoshop skills walker...is there something you are NOT good at?

(i am betting this guy is a killer soccer player!)
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Re: A bus stop is served by express buses, which run every hour at ten min  [#permalink]

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28 Jan 2008, 13:42
is there something you are NOT good at?

(i am betting this guy is a killer soccer player!)

No . If I were a killer soccer player I would play in Manchester United and have a lot of money!
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Re: A bus stop is served by express buses, which run every hour at ten min  [#permalink]

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28 Jan 2008, 14:25
30 sec solution: 1-(4*6+5)/60 = 31/60
Intern
Joined: 03 Jan 2014
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Re: A bus stop is served by express buses, which run every hour at ten min  [#permalink]

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25 Jan 2014, 07:06
At minutes 10, 20, 35 and 50 - wouldnt you have to wait zero minutes for the bus.

Which is why the calculation should not include those 4 minutes. In other words the sum should be: 8 + 8 + 8 + 3 = 27

And the probability = 27/60?
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Re: A bus stop is served by express buses, which run every hour at ten min  [#permalink]

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20 Oct 2014, 15:59
I am confused because I have a different answer...

|----5---10----20----30----35----40-----50----|

10,10,10,10 are the only open times it is possible to wait 6+ minutes

It is allowed 6 minutes that the person can wait before they are counted

4+4+4+4 = 16/60 = 4/15

Yet this is wrong?
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Re: A bus stop is served by express buses, which run every hour at ten min  [#permalink]

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20 Oct 2014, 20:42
1
At minutes 10, 20, 35 and 50 - wouldnt you have to wait zero minutes for the bus.

Which is why the calculation should not include those 4 minutes. In other words the sum should be: 8 + 8 + 8 + 3 = 27

And the probability = 27/60?

Say, 6:10 am is a point in time. It does not represent a whole minute.
6:10 to 6:11 represents a minute.
A bus arrives at 6:10 and the next one arrives at 6:20. A person who reaches the bus stop between 6:10 to 6:14 will need to wait for more than 6 mins.
6:10 to 6:14 represents 4 mins:
6:10 to 6:11,
6:11 to 6:12,
6:12 to 6:13 and
6:13 to 6:14

Similarly, a person arriving between 6:20 and 6:29 will need to wait for more than 6 mins. This time interval is 9 mins.
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Re: A bus stop is served by express buses, which run every hour at ten min  [#permalink]

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20 Oct 2014, 20:52
1
silhouette wrote:
I am confused because I have a different answer...

|----5---10----20----30----35----40-----50----|

10,10,10,10 are the only open times it is possible to wait 6+ minutes

It is allowed 6 minutes that the person can wait before they are counted

4+4+4+4 = 16/60 = 4/15

Yet this is wrong?

How did you get 30 and 40? The express buses run every hour starting at 10 mins past. So the express buses run only at 10 mins past.
Local buses run every 15 mins starting at 5 mins past so they run at 5, 20, 35 and 50 mins past the hour.

So buses run at following mins past the hour:
...5....10...20....35....50

This means a person arriving between 10 and 14, 20 and 29, 35 and 44, and 50 and 59 must wait for more than 6 mins.
4 + 9 + 9+ 9 = 31 mins

Probability = 31/60
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Re: A bus stop is served by express buses, which run every hour at ten min  [#permalink]

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21 Oct 2014, 19:29
VeritasPrepKarishma wrote:
How did you get 30 and 40?

I thought the buses came every ten minutes! But now I see where I was wrong. Thank you for explaining. Your insight is always appreciated. Thank you!!
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Re: A bus stop is served by express buses, which run every hour at ten min  [#permalink]

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19 Sep 2019, 14:50
silhouette wrote:
I am confused because I have a different answer...

|----5---10----20----30----35----40-----50----|

10,10,10,10 are the only open times it is possible to wait 6+ minutes

It is allowed 6 minutes that the person can wait before they are counted

4+4+4+4 = 16/60 = 4/15

Yet this is wrong?

How did you get 30 and 40? The express buses run every hour starting at 10 mins past. So the express buses run only at 10 mins past.
Local buses run every 15 mins starting at 5 mins past so they run at 5, 20, 35 and 50 mins past the hour.

So buses run at following mins past the hour:
...5....10...20....35....50

This means a person arriving between 10 and 14, 20 and 29, 35 and 44, and 50 and 59 must wait for more than 6 mins.
4 + 9 + 9+ 9 = 31 mins

Probability = 31/60

If he arrives at 6:14 , then he will have to wait for 6 minutes as the next bus is at 6:20.
Why are you then including 6:14 ? We need those time-instants for which wait-period is more than 6 minutes.
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Re: A bus stop is served by express buses, which run every hour at ten min  [#permalink]

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19 Sep 2019, 20:04
sayan640 wrote:
silhouette wrote:
I am confused because I have a different answer...

|----5---10----20----30----35----40-----50----|

10,10,10,10 are the only open times it is possible to wait 6+ minutes

It is allowed 6 minutes that the person can wait before they are counted

4+4+4+4 = 16/60 = 4/15

Yet this is wrong?

How did you get 30 and 40? The express buses run every hour starting at 10 mins past. So the express buses run only at 10 mins past.
Local buses run every 15 mins starting at 5 mins past so they run at 5, 20, 35 and 50 mins past the hour.

So buses run at following mins past the hour:
...5....10...20....35....50

This means a person arriving between 10 and 14, 20 and 29, 35 and 44, and 50 and 59 must wait for more than 6 mins.
4 + 9 + 9+ 9 = 31 mins

Probability = 31/60

If he arrives at 6:14 , then he will have to wait for 6 minutes as the next bus is at 6:20.
Why are you then including 6:14 ? We need those time-instants for which wait-period is more than 6 minutes.

Express: 6:10, 7:10, 8:10, 9:10 ...
Local: 6:05, 6:20, 6:35, 6:50, 7:05, 7:20, 7:35, 7:50 ...

If passenger arrives in these time slots between 6:00 to 7:00, he will need to wait more than 6 mins.
6:10 to 6:14 (arrives just a microsecond before the clock turns 6:14 so the minute of 6:13 to 6:14 is also added)
From 6:10 to 6:11, 1 min
from 6:11 to 6:12, 1 min
from 6:12 to 6:13, 1 min
from 6:13 to 6:14, 1 min
Total 4 mins from 6:10 to 6:14.
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Re: A bus stop is served by express buses, which run every hour at ten min  [#permalink]

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21 Sep 2019, 10:15
sayan640 wrote:
silhouette wrote:
I am confused because I have a different answer...

|----5---10----20----30----35----40-----50----|

10,10,10,10 are the only open times it is possible to wait 6+ minutes

It is allowed 6 minutes that the person can wait before they are counted

4+4+4+4 = 16/60 = 4/15

Yet this is wrong?

How did you get 30 and 40? The express buses run every hour starting at 10 mins past. So the express buses run only at 10 mins past.
Local buses run every 15 mins starting at 5 mins past so they run at 5, 20, 35 and 50 mins past the hour.

So buses run at following mins past the hour:
...5....10...20....35....50

This means a person arriving between 10 and 14, 20 and 29, 35 and 44, and 50 and 59 must wait for more than 6 mins.
4 + 9 + 9+ 9 = 31 mins

Probability = 31/60

If he arrives at 6:14 , then he will have to wait for 6 minutes as the next bus is at 6:20.
Why are you then including 6:14 ? We need those time-instants for which wait-period is more than 6 minutes.

Express: 6:10, 7:10, 8:10, 9:10 ...
Local: 6:05, 6:20, 6:35, 6:50, 7:05, 7:20, 7:35, 7:50 ...

If passenger arrives in these time slots between 6:00 to 7:00, he will need to wait more than 6 mins.
6:10 to 6:14 (arrives just a microsecond before the clock turns 6:14 so the minute of 6:13 to 6:14 is also added)
From 6:10 to 6:11, 1 min
from 6:11 to 6:12, 1 min
from 6:12 to 6:13, 1 min
from 6:13 to 6:14, 1 min
Total 4 mins from 6:10 to 6:14.[/quote]

VeritasKarishma maa'm, Why do you say "........from exact 6:10 to 6:11 ..." ?
Why are you considering the "6:10 " moment....?There is an express bus at 6:10 ...right ?

I apologize if I am over-analyzing.
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Re: A bus stop is served by express buses, which run every hour at ten min  [#permalink]

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22 Sep 2019, 21:33
sayan640 wrote:
VeritasKarishma maa'm, Why do you say "........from exact 6:10 to 6:11 ..." ?
Why are you considering the "6:10 " moment....?There is an express bus at 6:10 ...right ?

I apologize if I am over-analyzing.

It's the moment right after 6:10. Say a nano second after 6:10.
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Re: A bus stop is served by express buses, which run every hour at ten min   [#permalink] 22 Sep 2019, 21:33
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