Permutation and Combination

Expert replies

pareekbharat86: Master | Next Rank: 500 Posts; Posts: 168; Joined: Thu Nov 01, 2012 7:43 pm; Thanked: 1 times

by pareekbharat86 » Tue Dec 03, 2013 6:41 am

Each of 4 bags contains 25 blue disks, 25 green disks, 25 orange disks, 25 yellow disks, and nothing else. If one disk is chosen at random from each of the four bags, what is the probability that the number of blue disks chosen will be no less than 1 and no greater than 3?
a. 1/16
b. 41/128
c. 87/128
d. 225/256
e.255/256

OA is C

This is an SOS. I fare very poorly with probability and permutation & combinations. I just can't seem to get them right. Can someone please suggest some good material (book or online) so that I can stop fearing these questions. I really want to conquer this before the D-day.

Thanks,
Bharat.

Source: Beat The GMAT — Problem Solving | Tue Dec 03, 2013 6:41 am

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 » Tue Dec 03, 2013 7:06 am

pareekbharat86 wrote:Each of 4 bags contains 25 blue disks, 25 green disks, 25 orange disks, 25 yellow disks, and nothing else. If one disk is chosen at random from each of the four bags, what is the probability that the number of blue disks chosen will be no less than 1 and no greater than 3?
a. 1/16
b. 41/128
c. 87/128
d. 225/256
e.255/256

OA is C
.

Here:
A GOOD outcome is selecting 1, 2, or 3 blue disks.
A BAD outcome is selecting no blue disks or 4 blue disks.

P(good outcome) = 1 - P(bad outcome).

In each bag, 1/4 of the disks are blue, while 3/4 are not blue.
P(4 non-blue disks) = 3/4 * 3/4 * 3/4 * 3/4 = 81/256.
P(4 blue disks) = 1/4 * 1/4 * 1/4 * 1/4 = 1/256.
Thus:
P(good outcome) = 1 - (81/256 + 1/256) = 174/256 = 87/128.

The correct answer is C.

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

Mathsbuddy: Master | Next Rank: 500 Posts; Posts: 447; Joined: Fri Nov 08, 2013 7:25 amFollowed by: 1 member; Thanked: 25 times

by Mathsbuddy » Tue Dec 03, 2013 9:23 am

A = P(no blue) = (3/4)^4
B = P(4 blue) = (1/4)^4

P(A or B) = A + B

Also P(1, 2 or 3 blue) = P(Not A or B) = 1 - (A + B)

= 1 - (3/4)^4 - (1/4)^4

= (4^4 - 3^4 - 1^4)/(4^4)

= (256 - 81 - 1) /256

= 174/256 = 87/128

ANSWER C.

Featured schoolRound 2 closes Jan 7, 2027 53 days left

Chicago Booth

Since 1982, 10 Booth faculty members have received the Nobel Prize in Economic Sciences, more than any other business school.

#3
U.S. News rank: $175,000
Median base salary: 670
Average GMAT Focus: 635
Students in the class

Apply to Booth Visit chicagobooth.edu See the full profile

Photo: Warren LeMay, CC BY-SA 2.0

GMAT Course Reviews

563 reviews

1168 reviews

431 reviews

359 reviews

147 reviews

5/5

5 Star (563 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