Probability Problem

Expert replies

Sak32: Senior | Next Rank: 100 Posts; Posts: 30; Joined: Mon Oct 14, 2013 11:06 am

by Sak32 » Wed Nov 06, 2013 2:30 am

A book contains 732 pages numbered 1,2....732. If a student randomly opens the book, whats is the probability that the page number contains digit 1?

I had 246/732 for an answer and wanted to make sure its the right answer.

Like this post

Source: Beat The GMAT — Problem Solving | Wed Nov 06, 2013 2:30 am

ganeshrkamath: Master | Next Rank: 500 Posts; Posts: 283; Joined: Sun Jun 23, 2013 11:56 pmFollowed by: 26 members; Location: Bangalore, India; Thanked: 97 times; GMAT Score:750

by ganeshrkamath » Wed Nov 06, 2013 2:54 am

Sak32 wrote:A book contains 732 pages numbered 1,2....732. If a student randomly opens the book, whats is the probability that the page number contains digit 1?

I had 246/732 for an answer and wanted to make sure its the right answer.

0xy : 0x1, 01x => 10 + 10 - 1 = 19
1xy : 100
2xy : 19
3xy : 19
4xy : 19
5xy : 19
6xy : 19
700 to 732: 1 + 10 + 2 = 13

Total = 19*7 + 100 + 13 = 133 + 100 + 13
= 246

EDIT:
Total = 19*6 + 100 + 13 = 114 + 100 + 13
= 227

Probability = 227/732

Cheers

Last edited by ganeshrkamath on Wed Nov 06, 2013 11:12 am, edited 1 time in total.

Every job is a self-portrait of the person who did it. Autograph your work with excellence.

Kelley School of Business (Class of 2016)
GMAT Score: 750 V40 Q51 AWA 5 IR 8
https://www.beatthegmat.com/first-attemp ... tml#688494

Like this post

theCodeToGMAT: Legendary Member; Posts: 1556; Joined: Tue Aug 14, 2012 11:18 pmFollowed by: 34 members; Thanked: 448 times; GMAT Score:650

by theCodeToGMAT » Wed Nov 06, 2013 2:58 am

Pages 732

_ _ _

1 in Unit digit = 730/10 = 73 + 1 = 74

1 in Ten's Digit = 700/10 = 70 + 10 = 80

1 in Hundred's Digit = 100

So total = 100 + 74 + 80 = 254

So, 254/732

R A H U L

Like this post

ganeshrkamath: Master | Next Rank: 500 Posts; Posts: 283; Joined: Sun Jun 23, 2013 11:56 pmFollowed by: 26 members; Location: Bangalore, India; Thanked: 97 times; GMAT Score:750

by ganeshrkamath » Wed Nov 06, 2013 3:03 am

theCodeToGMAT wrote:Pages 732

_ _ _

1 in Unit digit = 730/10 = 73 + 1 = 74

1 in Ten's Digit = 700/10 = 70 + 10 = 80

1 in Hundred's Digit = 100

So total = 100 + 74 + 80 = 254

So, 254/732

Remove x11 from the total
254 - 8 = 246

Cheers

Like this post

theCodeToGMAT: Legendary Member; Posts: 1556; Joined: Tue Aug 14, 2012 11:18 pmFollowed by: 34 members; Thanked: 448 times; GMAT Score:650

by theCodeToGMAT » Wed Nov 06, 2013 3:41 am

I believe the answer must be 227/732 because we need probability of "1" in selected number.. so, we must consider total number of numbers which contain "1"..

So,

0 - 99 ==> _ _ ==> 10 + 10 = 20
100 - 200 ==> _ _ _ ==> 100 + 10 + 10 = 120
201 - 300 ==> _ _ _ ==> 0 + 10 + 10
301 - 400 ==> _ _ _ ==> 0 + 10 + 10
401 - 500 ==> _ _ _ ==> 0 + 10 + 10
501 - 600 ==> _ _ _ ==> 0 + 10 + 10
601 - 700 ==> _ _ _ ==> 0 + 10 + 10
701 - 732 ==> _ _ _ ==> _ + 10 + 4

Occurrence of _11 = 7 (11,211,311,411,511,611,711)
Occurrence of 1_1 = 9 (101,121,131,141,151,161,171,181,191)
Occurrence of 11_ = 9 (110,112,113......119)
occurrence of 111 = 1 (we need to do -2)

So, 254 - 7 - 9 - 9 -2 = 227

227/732

R A H U L

Like this post

GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Wed Nov 06, 2013 4:01 am

Sak32 wrote:A book contains 732 pages numbered 1,2....732. If a student randomly opens the book, whats is the probability that the page number contains digit 1?

I had 246/732 for an answer and wanted to make sure its the right answer.

Pages between 000 and 699, inclusive, that do NOT include 1:
Number of options for the hundreds place = 6. (Any digit 0-6 but 1.)
Number of options for the tens place = 9. (Any digit 0-9 but 1.)
Number of options for the units place = 9. (Any digit 0-9 but 1.)
To combine these options, we multiply:
6*9*9 = 486.

Pages between 000 and 699 that DO include 1:
Since 486 of the 700 pages do NOT include 1, the number of pages that DO include 1 = 700-486 = 214.

Pages between 700 and 732, inclusive, that include 1:
701
710 - 719
721
731
Total = 13.

Thus:
Total number of pages that include 1 = 214+13 = 227.
P(page includes 1) = 227/732.

Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.

As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.

For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3

Like this post

ganeshrkamath: Master | Next Rank: 500 Posts; Posts: 283; Joined: Sun Jun 23, 2013 11:56 pmFollowed by: 26 members; Location: Bangalore, India; Thanked: 97 times; GMAT Score:750

by ganeshrkamath » Wed Nov 06, 2013 11:13 am

ganeshrkamath wrote:Probability = 227/732

Edited above.

Cheers

Like this post

Post new topic Post Reply

• Page 1 of 1

GMAT Course Reviews

559 reviews

1168 reviews

431 reviews

359 reviews

147 reviews

5/5

5 Star (560 Reviews)

"Target Test Prep is the closest to the official version of the GMAT exam, about 99% accuracy in terms of the quality and quantity of information. The course has excellently created singular sets of focused lessons and tests for every possible topic that one could come across in the official GMAT exam."

"The TTP course maximizes the efficiency of the time you spend studying. It will take time and effort but I could almost guarantee that if you complete the course exactly as it is laid out you will get an amazing score. They also have a very responsive team willing to help with any questions you might have."

"TTP has two things that I think no other test prep company offers: A teaching approach that reinforces understanding and an attitude that will give you the mental preparedness needed to succeed on the test. TTP gives you a deep understanding of the concept you need to know while teaching you how to think."

Write a Review