Hi there,
This problem may be done pretty quick and using only GMAT´s level of Maths... insight is necessary, though.
I hope you enjoy it!
Best Regards,
Fábio.
Problem: A fair (6-faces) die is thrown repeatedly, till the number "2" appears for the 7th time. What is the probability that this occurs EXACTLY when you are throwing the die for the 10th time ?
Hint: [spoiler]exactly six "2"´s must appear in the first 9 results...[/spoiler]
Nice probab. problem!
This topic has expert replies
- fskilnik@GMATH
- GMAT Instructor
- Posts: 1449
- Joined: Sat Oct 09, 2010 2:16 pm
- Thanked: 59 times
- Followed by:33 members
Fabio Skilnik :: GMATH method creator ( Math for the GMAT)
English-speakers :: https://www.gmath.net
Portuguese-speakers :: https://www.gmath.com.br
English-speakers :: https://www.gmath.net
Portuguese-speakers :: https://www.gmath.com.br
- neerajkumar1_1
- Master | Next Rank: 500 Posts
- Posts: 270
- Joined: Wed Apr 07, 2010 9:00 am
- Thanked: 24 times
- Followed by:2 members
- fskilnik@GMATH
- GMAT Instructor
- Posts: 1449
- Joined: Sat Oct 09, 2010 2:16 pm
- Thanked: 59 times
- Followed by:33 members
Yes!! Congrats, neerajkumar1_1.neerajkumar1_1 wrote:is it
1/6 * (1/6)^6 * (5/6)^3 * 9!/(6! 3!)
Fabio Skilnik :: GMATH method creator ( Math for the GMAT)
English-speakers :: https://www.gmath.net
Portuguese-speakers :: https://www.gmath.com.br
English-speakers :: https://www.gmath.net
Portuguese-speakers :: https://www.gmath.com.br
- sanju09
- GMAT Instructor
- Posts: 3650
- Joined: Wed Jan 21, 2009 4:27 am
- Location: India
- Thanked: 267 times
- Followed by:80 members
- GMAT Score:760
and...
What is the probability that a letter chosen from the word PROBABILITY is between the letters B and T of the original spelling?
~just made
What is the probability that a letter chosen from the word PROBABILITY is between the letters B and T of the original spelling?
~just made
The mind is everything. What you think you become. -Lord Buddha
Sanjeev K Saxena
Quantitative Instructor
The Princeton Review - Manya Abroad
Lucknow-226001
www.manyagroup.com
Sanjeev K Saxena
Quantitative Instructor
The Princeton Review - Manya Abroad
Lucknow-226001
www.manyagroup.com
- fskilnik@GMATH
- GMAT Instructor
- Posts: 1449
- Joined: Sat Oct 09, 2010 2:16 pm
- Thanked: 59 times
- Followed by:33 members
Nice one, sanju9... not for the weak-of-heart, uh?!sanju09 wrote: What is the probability that a letter chosen from the word PROBABILITY is between the letters B and T of the original spelling?
What I like most is the fact that we must take into account the number of repetitions of the letter chosen (from the word PROBABILITY) beforehand! REALLY nice... if nobody comes first, I´ll give my shoot on sunday or monday, ok?!
Have a nice weekend, neerajkumar1_1 too!
Regards,
Fabio.
Fabio Skilnik :: GMATH method creator ( Math for the GMAT)
English-speakers :: https://www.gmath.net
Portuguese-speakers :: https://www.gmath.com.br
English-speakers :: https://www.gmath.net
Portuguese-speakers :: https://www.gmath.com.br
- sanju09
- GMAT Instructor
- Posts: 3650
- Joined: Wed Jan 21, 2009 4:27 am
- Location: India
- Thanked: 267 times
- Followed by:80 members
- GMAT Score:760
I´ll give my toot on sunday or monday, ok?!vijchid wrote:Is the answer 6/11? Sanju?
The mind is everything. What you think you become. -Lord Buddha
Sanjeev K Saxena
Quantitative Instructor
The Princeton Review - Manya Abroad
Lucknow-226001
www.manyagroup.com
Sanjeev K Saxena
Quantitative Instructor
The Princeton Review - Manya Abroad
Lucknow-226001
www.manyagroup.com
The distinct letter in the word "PROBABILITY" - 9 ( P,R,O,B,A,I,L,T,Y) .
so number of ways of choosing a letter from the word = 9c1 = 9
Distinct latters in the word "BABILIT" = 5 (B,A,I,L,T)
Number of ways of choosing a letter from "BABILIT" = 5 .
So required prob= 5/9 . OA pls
so number of ways of choosing a letter from the word = 9c1 = 9
Distinct latters in the word "BABILIT" = 5 (B,A,I,L,T)
Number of ways of choosing a letter from "BABILIT" = 5 .
So required prob= 5/9 . OA pls
- sanju09
- GMAT Instructor
- Posts: 3650
- Joined: Wed Jan 21, 2009 4:27 am
- Location: India
- Thanked: 267 times
- Followed by:80 members
- GMAT Score:760
Please refer to the question againbitsho wrote:The distinct letter in the word "PROBABILITY" - 9 ( P,R,O,B,A,I,L,T,Y) .
so number of ways of choosing a letter from the word = 9c1 = 9
Distinct latters in the word "BABILIT" = 5 (B,A,I,L,T)
Number of ways of choosing a letter from "BABILIT" = 5 .
So required prob= 5/9 . OA pls
The mind is everything. What you think you become. -Lord Buddha
Sanjeev K Saxena
Quantitative Instructor
The Princeton Review - Manya Abroad
Lucknow-226001
www.manyagroup.com
Sanjeev K Saxena
Quantitative Instructor
The Princeton Review - Manya Abroad
Lucknow-226001
www.manyagroup.com
- neerajkumar1_1
- Master | Next Rank: 500 Posts
- Posts: 270
- Joined: Wed Apr 07, 2010 9:00 am
- Thanked: 24 times
- Followed by:2 members
I dont know from where u come up with these questions.. but they are sure fun to solve..sanju09 wrote:and...
What is the probability that a letter chosen from the word PROBABILITY is between the letters B and T of the original spelling?
~just made
let me see if i can get it..
the word is PROBABILITY
we want the probability that a letter chosen from the original spelling is between B & T
now since there are 2 B's and they are going to create confusion, it will be simpler solving 1 - required..
letters which will not be between B & T will be PROBTY
but since B is already between B & T we can count B... so the not required letters will be PROTY
hence the required prob will be = 1 - 5/11 = 6/11
Let me know sanju09..
- fskilnik@GMATH
- GMAT Instructor
- Posts: 1449
- Joined: Sat Oct 09, 2010 2:16 pm
- Thanked: 59 times
- Followed by:33 members
Funny thing... I understood a COMPLETELY different problem... I will try to create the question stem that I believed was sanju´s idea... and wait for his feedback before giving my (try of) solution...sanju09 wrote:What is the probability that a letter chosen from the word PROBABILITY is between the letters B and T of the original spelling?
Let x be one of the letters (randomly) chosen from the word PROBABILITY.
If an anagram of this word is randomly chosen, what is the probability that the chosen letter appears between the 5th and 9th positions (from left to right), both of them included?
Best Regards,
Fabio.
Fabio Skilnik :: GMATH method creator ( Math for the GMAT)
English-speakers :: https://www.gmath.net
Portuguese-speakers :: https://www.gmath.com.br
English-speakers :: https://www.gmath.net
Portuguese-speakers :: https://www.gmath.com.br