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

It is currently 16 Jul 2018, 13:31

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

A man is known to speak truth 3 out of 4 times. He throws

  post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
Senior Manager
Senior Manager
User avatar
Joined: 19 Nov 2007
Posts: 433
GMAT ToolKit User
A man is known to speak truth 3 out of 4 times. He throws [#permalink]

Show Tags

New post 13 Aug 2008, 10:47
A man is known to speak truth 3 out of 4 times. He throws die and reports that it is a 6. The probability that it is actually a 6 is

A) 3/4
B) 5/8
C) 2/5
D) 3/5
E) 4/5

--== Message from GMAT Club Team ==--

This is not a quality discussion. It has been retired.

If you would like to discuss this question please re-post it in the respective forum. Thank you!

To review the GMAT Club's Forums Posting Guidelines, please follow these links: Quantitative | Verbal Please note - we may remove posts that do not follow our posting guidelines. Thank you.

_________________

-Underline your question. It takes only a few seconds!
-Search before you post.

Manager
Manager
avatar
Joined: 15 Jul 2008
Posts: 205
Re: probabilty [#permalink]

Show Tags

New post 13 Aug 2008, 19:18
nice trap question. agree with 3/4
Director
Director
avatar
Joined: 10 Sep 2007
Posts: 913
Re: probabilty [#permalink]

Show Tags

New post 13 Aug 2008, 19:39
Prob that its a 6 and he speaks truth :- 3/4 * 1/6 = 3/24

Now what is the prob of reporting a 6 on a dice when it is a lie = 1/4 (speaking a lie) * 5/6 (prob of no. other than 6) * 1/5 (lieing the number as 6 and not telling any othe number except the actual no.) = 5/120 = 1/24

Thus the prob of reporting no. as 6 (total lie + truth) = 3/24 + 1/24 = 4/24 = 1/6

Thus prob of actually having 6 when reported so is = 3/24/1/6 = 3/4

Answer A.
VP
VP
avatar
Joined: 28 Dec 2005
Posts: 1482
Re: probabilty [#permalink]

Show Tags

New post 13 Aug 2008, 20:11
actually, i just thought of it like this: if he is telling the truth 3 out of 4 times, that means hes telling the truth 75% of the time. That means on any give statement, he is telling the truth 75% of the time .... i.e. 0.75, which is still just 3/4
Director
Director
avatar
Joined: 27 May 2008
Posts: 531
Re: probabilty [#permalink]

Show Tags

New post 13 Aug 2008, 21:43
:) good question

what if i change the question to

"A man is known to speak truth 3 out of 4 times. He throws a die. What is the probability that he'll report a 6."
Director
Director
avatar
Joined: 10 Sep 2007
Posts: 913
Re: probabilty [#permalink]

Show Tags

New post 13 Aug 2008, 21:50
durgesh79 wrote:
:) good question

what if i change the question to

"A man is known to speak truth 3 out of 4 times. He throws a die. What is the probability that he'll report a 6."

Prob that its a 6 and he speaks truth :- 3/4 * 1/6 = 3/24

Now what is the prob of reporting a 6 on a dice when it is a lie = 1/4 (speaking a lie) * 5/6 (prob of no. other than 6) * 1/5 (lieing the number as 6 and not telling any othe number except the actual no.) = 5/120 = 1/24

Thus the prob of reporting no. as 6 (total lie + truth) = 3/24 + 1/24 = 4/24 = 1/6
Director
Director
avatar
Joined: 27 May 2008
Posts: 531
Re: probabilty [#permalink]

Show Tags

New post 13 Aug 2008, 21:55
abhijit_sen wrote:
durgesh79 wrote:
:) good question

what if i change the question to

"A man is known to speak truth 3 out of 4 times. He throws a die. What is the probability that he'll report a 6."

Prob that its a 6 and he speaks truth :- 3/4 * 1/6 = 3/24

Now what is the prob of reporting a 6 on a dice when it is a lie = 1/4 (speaking a lie) * 5/6 (prob of no. other than 6) * 1/5 (lieing the number as 6 and not telling any othe number except the actual no.) = 5/120 = 1/24

Thus the prob of reporting no. as 6 (total lie + truth) = 3/24 + 1/24 = 4/24 = 1/6


i knew that you'll catch the trap :)

I missed it (highlighted) the first time and ended up with 1/3 .. then i thought the sum of all porbable cases ( reporting 1,2,3,4,5 or 6 ) should be 1 .... whatever is the % chances of speaking truth ...

so the probability should be 1/6... and you proved it mathematically ... thanks
Intern
Intern
avatar
Joined: 12 Aug 2008
Posts: 4
Re: probabilty [#permalink]

Show Tags

New post 14 Aug 2008, 12:01
Could someone please clarify what the trap was in this question and detail any other such probability traps that may be out there. It would be very helpful.

Thank you,
Vin
Expert Post
GMAT Tutor
avatar
S
Joined: 24 Jun 2008
Posts: 1345
Re: probabilty [#permalink]

Show Tags

New post 14 Aug 2008, 12:10
There's an assumption here that when this guy lies, he tells a plausible lie. When he lies, why wouldn't he say 'I rolled a 41', or 'I didn't roll the die at all'?

(I'm half-joking, of course)
_________________

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
Joined: 22 Jul 2008
Posts: 140
Re: probabilty [#permalink]

Show Tags

New post 14 Aug 2008, 12:45
I didn't quite understand the solution. Should the total probability not be 1? What I mean is, that the Probability of Truth, let's say, Pt and the Probability of Lie, say, Pl, should add up to 1. In your solution Pt is 3/24 and Pl is 1/24. They add up to only 4/24 or 1/6. Isn't that right?

I am not sure but I feel the answer should be different. By my logic I am getting the answer as 4/5. I could be wrong, but if I am, please correct me.
From the question, it seems there are 3 truths and 1 false in every 4 times.
Probability of False is 1*1*1*1/2^4 i.e., 1/16 (This is the same as tossing a coin, since there are only 2 options). Therefore, the probability of truth is 1-1/16 = 15/16 for a single event.
Given Probability for a single event is 3/4.
Therefore, the total Probability is 3/4 / 15/16 = 4/5.
Manager
Manager
avatar
Joined: 15 Jul 2008
Posts: 205
Re: probabilty [#permalink]

Show Tags

New post 14 Aug 2008, 17:52
durgesh79 wrote:
abhijit_sen wrote:
durgesh79 wrote:
:) good question

what if i change the question to

"A man is known to speak truth 3 out of 4 times. He throws a die. What is the probability that he'll report a 6."

Prob that its a 6 and he speaks truth :- 3/4 * 1/6 = 3/24

Now what is the prob of reporting a 6 on a dice when it is a lie = 1/4 (speaking a lie) * 5/6 (prob of no. other than 6) * 1/5 (lieing the number as 6 and not telling any othe number except the actual no.) = 5/120 = 1/24

Thus the prob of reporting no. as 6 (total lie + truth) = 3/24 + 1/24 = 4/24 = 1/6


i knew that you'll catch the trap :)

I missed it (highlighted) the first time and ended up with 1/3 .. then i thought the sum of all porbable cases ( reporting 1,2,3,4,5 or 6 ) should be 1 .... whatever is the % chances of speaking truth ...

so the probability should be 1/6... and you proved it mathematically ... thanks


This question, in its current form is vague. I would be tempted to say that the 1/6*3/4 only. B-cos the solution assumes that his lie is restricted to numbers 1-6. His lies can actually be limitless...
Director
Director
avatar
Joined: 14 Aug 2007
Posts: 695
Re: probabilty [#permalink]

Show Tags

New post 14 Aug 2008, 19:14
durgesh79 wrote:
abhijit_sen wrote:
durgesh79 wrote:
:) good question

what if i change the question to

"A man is known to speak truth 3 out of 4 times. He throws a die. What is the probability that he'll report a 6."

Prob that its a 6 and he speaks truth :- 3/4 * 1/6 = 3/24

Now what is the prob of reporting a 6 on a dice when it is a lie = 1/4 (speaking a lie) * 5/6 (prob of no. other than 6) * 1/5 (lieing the number as 6 and not telling any othe number except the actual no.) = 5/120 = 1/24

Thus the prob of reporting no. as 6 (total lie + truth) = 3/24 + 1/24 = 4/24 = 1/6


i knew that you'll catch the trap :)

I missed it (highlighted) the first time and ended up with 1/3 .. then i thought the sum of all porbable cases ( reporting 1,2,3,4,5 or 6 ) should be 1 .... whatever is the % chances of speaking truth ...

so the probability should be 1/6... and you proved it mathematically ... thanks


the explanation given by abhijit_sen is the most apt mathematically.

I was just wondering if the probability of man saying a truth or lie really matters for Durgesh79's question.
For predicting any one number on a die the probability will be 1/6

Just wanted to discuss, I may be "perfectly" wrong :)
Director
Director
avatar
Joined: 27 May 2008
Posts: 531
Re: probabilty [#permalink]

Show Tags

New post 14 Aug 2008, 20:56
OK, I'll correct the "my version" of question.

A man is known to speak truth 3 out of 4 times. He throws a die. What is the probability that he'll report a 6 provided that he can not only report a possible outcome.

alpha : you are right, the probablity will be 1/6 only, it doesnt depend on the probability of speaking truth...
Manager
Manager
avatar
Joined: 15 Jul 2008
Posts: 205
Re: probabilty [#permalink]

Show Tags

New post 15 Aug 2008, 13:52
durgesh79 wrote:
OK, I'll correct the "my version" of question.

A man is known to speak truth 3 out of 4 times. He throws a die. What is the probability that he'll report a 6 provided that he can not only report a possible outcome.

alpha : you are right, the probablity will be 1/6 only, it doesnt depend on the probability of speaking truth...



Are the outcome of the die and the guy's reporting independent here ? Am confused because his lying or speaking truth is independent of die roll, but his actual report doesnt seem to be independent of the outcome of the die roll.
Director
Director
avatar
Joined: 27 May 2008
Posts: 531
Re: probabilty [#permalink]

Show Tags

New post 15 Aug 2008, 20:57
bhushangiri wrote:
durgesh79 wrote:
OK, I'll correct the "my version" of question.

A man is known to speak truth 3 out of 4 times. He throws a die. What is the probability that he'll report a 6 provided that he can not only report a possible outcome.

alpha : you are right, the probablity will be 1/6 only, it doesnt depend on the probability of speaking truth...



Are the outcome of the die and the guy's reporting independent here ? Am confused because his lying or speaking truth is independent of die roll, but his actual report doesnt seem to be independent of the outcome of the die roll.


i dont know if i understand your doubt but look at it this way

x is the probability of speaking truth, then 1-x is the probablity of not speaking truth.

probability of reporting a 6
= when actual is six and he is reporing 6 + when actual is some thing else (1,2,3,4,5) and he is not speaking truth and reporting 6.
= 1/6 * x + 5/6 * (1-x) * 1/5
= 1/6 -----> doesnt depend on x

this'll only work when he always reports one of the possible outcome .... that is clarified in the question.

--== Message from GMAT Club Team ==--

This is not a quality discussion. It has been retired.

If you would like to discuss this question please re-post it in the respective forum. Thank you!

To review the GMAT Club's Forums Posting Guidelines, please follow these links: Quantitative | Verbal Please note - we may remove posts that do not follow our posting guidelines. Thank you.
Re: probabilty   [#permalink] 15 Aug 2008, 20:57
Display posts from previous: Sort by

A man is known to speak truth 3 out of 4 times. He throws

  post reply Question banks Downloads My Bookmarks Reviews Important topics  

Moderator: chetan2u

Events & Promotions

PREV
NEXT


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®.