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

Question

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

Show Answer

Official Answer

B

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

walker · Accepted Answer

p=\frac{9+9+9+4}{60}=\frac{31}{60}

LM · Answer

P = (4/60) + ( 4/60) + ( 9/60) + ( 9/60) + (10/60) = 36/60 = 3/5

sondenso · Answer

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! :oops:

LM · Answer

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!

neelesh · Answer

Excellent explanation Walker.

Does this seem like a 2-minute type question ?

walker · Answer

I guess yes. But I spent more than 15 min to draw it in PhotoShop.... :writer

buffdaddy · Answer

It took about a minute,
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!)

walker · Answer

No

. If I were a killer soccer player I would play in Manchester United and have a lot of money!

maratikus · Answer

30 sec solution: 1-(4*6+5)/60 = 31/60

adaptari · Answer

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?

silhouette · Answer

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?

KarishmaB · Answer

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.

KarishmaB · Answer

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

silhouette · Answer

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!!

sayan640 · Answer

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.
 VeritasKarishma  ?

KarishmaB · Answer

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.

sayan640 · Answer

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.
 VeritasKarishma  ?

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.

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.
 VeritasKarishma 
 VeritasKarishma

KarishmaB · Answer

It's the moment right after 6:10. Say a nano second after 6:10.

Rebaz · Answer

This is the most annoying question i have ever seen and everyone assumes times slots inwhich someone arrives and has to wait, without explaing why? i mean why someone arrives at 06:14 etc....

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 mean which busstop does the passenger arrives? the express one or the local one and how do we know which one it is? I have never been so confused and angry at a question.

I donot even understand the question stem and the way it is formulated and what it is asking?

Goodluck!

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

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

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