GMAT Question of the Day - Daily to your Mailbox; hard ones only

It is currently 23 Jun 2018, 08:32

Close

GMAT Club Daily Prep

Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Close

Request Expert Reply

Confirm Cancel

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

Colleen times her morning commute such that there is an equal likeliho

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Intern
Intern
avatar
Joined: 21 Jun 2014
Posts: 34
GMAT ToolKit User Premium Member
Colleen times her morning commute such that there is an equal likeliho [#permalink]

Show Tags

New post Updated on: 26 May 2015, 05:33
11
00:00
A
B
C
D
E

Difficulty:

  75% (hard)

Question Stats:

49% (01:31) correct 51% (01:39) wrong based on 110 sessions

HideShow timer Statistics

Colleen times her morning commute such that there is an equal likelihood that she will arrive early or late to work on any given day. If she always arrives either early or late, what is the probability that Colleen will arrive late to work no more than twice during a five-day workweek?

(A) 1/4
(B) 15/32
(C) 1/2
(D) 1732
(E) 3/4

My Answer (B)
I made it look like Head and Tails questions and looked for answer, not more than two Heads
HTTTT + HHTTT
= 5c1/32 + 5c2/32 = 15/32 (But not correct answer)

Originally posted by sandeepmanocha on 25 May 2015, 13:44.
Last edited by Bunuel on 26 May 2015, 05:33, edited 1 time in total.
Renamed the topic, edited the question, added the OA and moved to PS forum.
Expert Post
2 KUDOS received
GMAT Tutor
avatar
S
Joined: 24 Jun 2008
Posts: 1345
Re: Colleen times her morning commute such that there is an equal likeliho [#permalink]

Show Tags

New post 25 May 2015, 15:04
2
sandeepmanocha wrote:
My Answer (B)
I made it look like Head and Tails questions and looked for answer, not more than two Heads
HTTTT + HHTTT
= 5c1/32 + 5c2/32 = 15/32 (But not correct answer)


Your thinking is right here, but you missed one case. If you think of it as a coinflip problem, it is also possible that all 5 flips are tails: TTTTT. Since that has a (1/2)^5 = 1/32 chance of happening, that's the reason your answer was too low by exactly 1/32.

There's a slightly faster way to do the problem. The probability she will be late at most 2 times is exactly the same as the probability she will be early at most 2 times. But those are all the possible scenarios, so each must happen 1/2 the time.
_________________

GMAT Tutor in Toronto

If you are looking for online GMAT math tutoring, or if you are interested in buying my advanced Quant books and problem sets, please contact me at ianstewartgmat at gmail.com

Intern
Intern
avatar
Joined: 21 Jun 2014
Posts: 34
GMAT ToolKit User Premium Member
Re: Colleen times her morning commute such that there is an equal likeliho [#permalink]

Show Tags

New post 25 May 2015, 15:54
IanStewart wrote:
Your thinking is right here, but you missed one case. If you think of it as a coinflip problem, it is also possible that all 5 flips are tails: TTTTT. Since that has a (1/2)^5 = 1/32 chance of happening, that's the reason your answer was too low by exactly 1/32.

Thanks for pointing, and yes AT MOST means, 0 or more upto given limit. It is going into my Tips :)

IanStewart wrote:
There's a slightly faster way to do the problem. The probability she will be late at most 2 times is exactly the same as the probability she will be early at most 2 times. But those are all the possible scenarios, so each must happen 1/2 the time.

Although I am not sure about this comment. Please can you elaborate on this?

Thanks
Expert Post
2 KUDOS received
GMAT Tutor
avatar
S
Joined: 24 Jun 2008
Posts: 1345
Re: Colleen times her morning commute such that there is an equal likeliho [#permalink]

Show Tags

New post 25 May 2015, 18:23
2
1
Say you flip a coin 5 times, and are asked two questions:

1. what's the probability you get more Heads than Tails?
2. what's the probability you get more Tails than Heads?

the answer to those two questions must be the same, because, since it's equally likely you get Heads or Tails on each toss, there's no logical reason why the answer to question 1 should be lower or higher than the answer to question 2.

But the situations in 1 and 2 are the only things that can possibly happen - we can't get an equal number of H and T if we flip a coin an odd number of times. And the probabilities of all the things that can happen must add up to 1. So we have two equal probabilities that add to 1, and both probabilities must be 1/2.

Notice that question 2, "what's the probability you get more Tails than Heads" is exactly the question you were answering: it's the same question as: "what's the probability you get at most 2 Heads if you flip a coin 5 times?"

So that's one way to see that the answer is 1/2 here without looking at any cases.
_________________

GMAT Tutor in Toronto

If you are looking for online GMAT math tutoring, or if you are interested in buying my advanced Quant books and problem sets, please contact me at ianstewartgmat at gmail.com

Manager
Manager
avatar
S
Joined: 29 May 2016
Posts: 122
Re: Colleen times her morning commute such that there is an equal likeliho [#permalink]

Show Tags

New post 10 Sep 2016, 05:17
probability that Colleen will arrive late to work no more than twice
what does that mean, shall i consider at-least one till max 2 than answer will be 15/32

but if we can consider even a zero case of late than answer will be be C 16/32= 1/2

please give the correct explanation
Intern
Intern
avatar
B
Joined: 26 Jan 2014
Posts: 9
Re: Colleen times her morning commute such that there is an equal likeliho [#permalink]

Show Tags

New post 21 May 2017, 16:16
mbaprep2016 wrote:
probability that Colleen will arrive late to work no more than twice
what does that mean, shall i consider at-least one till max 2 than answer will be 15/32

but if we can consider even a zero case of late than answer will be be C 16/32= 1/2

please give the correct explanation


Yes, you are right. At most 2 includes "not late even once" so the answer would be 15/32 + 1/32 = 1/2.
Senior Manager
Senior Manager
avatar
G
Joined: 24 Apr 2016
Posts: 333
Re: Colleen times her morning commute such that there is an equal likeliho [#permalink]

Show Tags

New post 22 May 2017, 12:34
Case 1: Colleen was late on 0 out of 5 days.

==> 1/2 * 1/2 * 1/2 * 1/2 * 1/2 = 1/32

Case 2: Colleen was late on 1 out of 5 days.

==> 1/2 * 1/2 * 1/2 * 1/2 * 1/2 * 5C1

==> 1/32 * 5 = 5/32

Case 3: Colleen was late on 2 out of 5 days.

==> 1/2 * 1/2 * 1/2 * 1/2 * 1/2 * 5C2

==> 1/32 * 10 = 5/16

Probability that Colleen will arrive late to work no more than twice during a five-day workweek

= 1/32 + 5/32 + 5/16 = 16/32 = 1/2

Answer is C
Re: Colleen times her morning commute such that there is an equal likeliho   [#permalink] 22 May 2017, 12:34
Display posts from previous: Sort by

Colleen times her morning commute such that there is an equal likeliho

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  


GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.