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

It is currently 16 Aug 2018, 20:44

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

Johnny the gambler tosses 6 plain dice. In order to win the jackpot, h

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

Hide Tags

Manager
Manager
avatar
Joined: 25 Mar 2011
Posts: 69
Johnny the gambler tosses 6 plain dice. In order to win the jackpot, h  [#permalink]

Show Tags

New post Updated on: 09 Aug 2015, 01:16
2
12
00:00
A
B
C
D
E

Difficulty:

  75% (hard)

Question Stats:

60% (02:21) correct 40% (02:32) wrong based on 96 sessions

HideShow timer Statistics

Johnny the gambler tosses 6 plain dice. In order to win the jackpot, he needs a 5 or 6 on exactly three of the dice. What are Johnny's chances to win?

A. 20×(2^2/3^6)
B. 10×(2^3/3^6)
C. 20×(2^3/3^5)
D. 20×(2^3/3^6)
E. 20×(2^2/3^5)

Originally posted by smodak on 26 Jun 2011, 12:09.
Last edited by reto on 09 Aug 2015, 01:16, edited 1 time in total.
Added AC's and Source + proper format
Senior Manager
Senior Manager
User avatar
Joined: 03 Mar 2010
Posts: 395
Schools: Simon '16 (M)
Re: Johnny the gambler tosses 6 plain dice. In order to win the jackpot, h  [#permalink]

Show Tags

New post 26 Jun 2011, 12:43
1
2
Probability of getting 5 = 1/6
Probability of getting 6 = 1/6
Probability of getting 5 or 6 = P(5) + P(6)- P(5 and 6)
P(5 and 6) = 0 Since getting 5 and 6 is mutually exclusive event. i.e you cannot get both.
Probability of getting 5 or 6 = P(5) + P(6)
\(= 1/6 +1/6 = 2/6 = 1/3\)

Probability of getting (1,2,3,4) = 1-Probability of getting 5 or 6 = \(1-1/3 = 2/3\)

Probability of getting 5 or 6 exactly three times = \((1/3) * (1/3) * (1/3) * (2/3) * (2/3) *(2/3)= 2^3/3^6\)

We need 5 or 6 to come exactly three times in sequence of 6 times dice roll.
(5 or 6) , (5 or 6), (5 or 6), (1,2,3,4), (1,2,3,4), (1,2,3,4)
we can get (5 or 6) in any order in 6 times for total of \(6C3= 20\)

Hence total ways = \(20 * 2^3/3^6\)
_________________

My dad once said to me: Son, nothing succeeds like success.

Manager
Manager
User avatar
Joined: 07 Oct 2010
Posts: 153
Re: Johnny the gambler tosses 6 plain dice. In order to win the jackpot, h  [#permalink]

Show Tags

New post 26 Jun 2011, 13:05
1
i have solved the example with normal principle of counting ...i.e. without using some formula or funda....

First of all the person tossed the dice 6 times hence the sample space would be 6^6

he got exactly 3 times either 5 or 6 i.e. 6C1+6C1 * 6C1+6C1 * 6C1+6C1 = 2*2*2

And in the remaining 3 tosses he got any number except 5 or 6 hence out of remaining 4 numbers he got any 1 = 4C1*4C1*4C1 = 4*4*4

hence in total of 6 tosses he got 2*2*2*4*4*4 = 2^9

Now, out of 6 tosses he got 5or6 in any 3 tosses thus it can be arranged in 6C3 ways = 20 ways

Now, Sample space is 6^6 , also, out of 6 tosses getting 5or6 is possible in 20 ways and results of the tosses are possible in 2^9 ways,

Thus chances of winning = 20 * 2^9 / 6^6 = 20* 2^9/ 2^6*3^6 = 20 * 2^3/ 3^6
Current Student
avatar
Joined: 26 May 2005
Posts: 528
Re: Johnny the gambler tosses 6 plain dice. In order to win the jackpot, h  [#permalink]

Show Tags

New post 26 Jun 2011, 21:47
2
smodak wrote:
Johnny the gambler tosses 6 plain dice. In order to win the jackpot he has to receive exactly 3 times a result of 5 or 6. What are Johnny's chances to win?

OA:
20×(2^3/3^6)


Please explain how you arrived at the answer:

Source: Master GMAT


I use binomial theorem :
chances of 5 or 6 = 2/6 = 1/3
other numbers = 1-1/3= 2/3
Binomial theorem = nCr (p)^r*(1-p)^n-r
= 6C3(1/3)^3)(2/3)^6-3
= 20* 2^3/3^6
Intern
Intern
avatar
Joined: 28 Mar 2011
Posts: 31
Re: Johnny the gambler tosses 6 plain dice. In order to win the jackpot, h  [#permalink]

Show Tags

New post 26 Jun 2011, 23:02
sudhir18n wrote:
smodak wrote:
Johnny the gambler tosses 6 plain dice. In order to win the jackpot he has to receive exactly 3 times a result of 5 or 6. What are Johnny's chances to win?

OA:
20×(2^3/3^6)


Please explain how you arrived at the answer:

Source: Master GMAT


I use binomial theorem :
chances of 5 or 6 = 2/6 = 1/3
other numbers = 1-1/3= 2/3
Binomial theorem = nCr (p)^r*(1-p)^n-r
= 6C3(1/3)^3)(2/3)^6-3
= 20* 2^3/3^6


A nice application of binomial theorem sudhir18n.
It did not strike me. :roll:

Thanks!

Regards,
Divya
Retired Moderator
avatar
Joined: 29 Apr 2015
Posts: 862
Location: Switzerland
Concentration: Economics, Finance
Schools: LBS MIF '19
WE: Asset Management (Investment Banking)
GMAT ToolKit User Premium Member
Re: Johnny the gambler tosses 6 plain dice. In order to win the jackpot, h  [#permalink]

Show Tags

New post 09 Aug 2015, 01:19
1
smodak wrote:
Johnny the gambler tosses 6 plain dice. In order to win the jackpot, he needs a 5 or 6 on exactly three of the dice. What are Johnny's chances to win?

A. 20×(2^2/3^6)
B. 10×(2^3/3^6)
C. 20×(2^3/3^5)
D. 20×(2^3/3^6)
E. 20×(2^2/3^5)


A nice question. I think it is worth of discussing again. Here I have the official answers:

This looks like a tough nugget, but let's break it down. First of all, look at one possible arrangement (h = 5 or 6, l = 1,2,3 or 4):

h,h,h,l,l,l (h=high, l=low)

The probability of getting 5 or 6 in a die toss is 1/6+1/6 = 1/3.
The probability of getting 1,2,3 or 4 in a die toss is 2/3.

So the odds of getting that particular arrangement are:

1/3*1/3*1/3*2/3*2/3*2/3 = 2^3/3^6

This is the chance for any given arrangement of three h and three l. However, this is only one possible scenario of having high results on three rolls. How many such scenarios exist?

What you need now is the number of possible arrangements: the number of ways of picking 3 high results out of 6 tosses. Order of choice doesn't matter, because you only care about which rolls are chosen - not the order you chose them in. For example, if you chose tosses 1,2,3 to yield high results, it does not matter in what order you chose them. Now that we have reduced the problem to a simple case of choosing k=3 out of n=6, order doesn't matter, use the Combinations formula:

6!/3!*3! = 20

So the probability that you're looking for is the number of arrangements times the probability of each arrangement.

Answer D

I am happy to help. :-)
_________________

Saving was yesterday, heat up the gmatclub.forum's sentiment by spending KUDOS!

PS Please send me PM if I do not respond to your question within 24 hours.

Senior Manager
Senior Manager
User avatar
G
Joined: 14 Dec 2017
Posts: 451
Re: Johnny the gambler tosses 6 plain dice. In order to win the jackpot, h  [#permalink]

Show Tags

New post 10 Jun 2018, 12:47
smodak wrote:
Johnny the gambler tosses 6 plain dice. In order to win the jackpot, he needs a 5 or 6 on exactly three of the dice. What are Johnny's chances to win?

A. 20×(2^2/3^6)
B. 10×(2^3/3^6)
C. 20×(2^3/3^5)
D. 20×(2^3/3^6)
E. 20×(2^2/3^5)


Probability of getting a 5 or 6 on a single dice toss = 1/6 + 1/6 = 2/6

Now Probability of getting a 5 or 6 on exactly 3 of the 6 dice tossed = (2/6) * (2/6) * (2/6) * (1-2/6) * (1-2/6) * (1-2/6) * (6!/3!*3!) = 20*(2^3/3^6)

Answer D.


Thanks,
GyM
Re: Johnny the gambler tosses 6 plain dice. In order to win the jackpot, h &nbs [#permalink] 10 Jun 2018, 12:47
Display posts from previous: Sort by

Johnny the gambler tosses 6 plain dice. In order to win the jackpot, h

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

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®.