Probability

BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

This topic has expert replies

Post new topic Post Reply

Previous Topic Next Topic

BTGmoderatorRO: Moderator; Posts: 772; Joined: Wed Aug 30, 2017 6:29 pm; Followed by:6 members

Probability

by BTGmoderatorRO » Sat Jan 20, 2018 5:16 am

Among a group of 2,500 people, 35 percent invest in municipal bonds, 18 percent invest in oil stocks, and 7 percent invest in both municipal bonds and oil stocks. If 1 person is to be randomly selected from the 2,500 people, what is the probability that the person selected will be one who invests in municipal bonds and NOT in oils stocks?

A) 950950

B) 725725

C) 720720

D) 21502150

E) 2750

OA is B
What is the best method to solve this? An Expert contribution will be appreciated. Thanks

Quote

Source: Beat The GMAT — Problem Solving | Sat Jan 20, 2018 5:16 am

EconomistGMATTutor: GMAT Instructor; Posts: 555; Joined: Wed Oct 04, 2017 4:18 pm; Thanked: 180 times; Followed by:12 members

Probability

by EconomistGMATTutor » Sat Jan 20, 2018 2:47 pm

Among a group of 2,500 people, 35 percent invest in municipal bonds, 18 percent invest in oil stocks, and 7 percent invest in both municipal bonds and oil stocks. If 1 person is to be randomly selected from the 2,500 people, what is the probability that the person selected will be one who invests in municipal bonds and NOT in oils stocks?

A) 950950

B) 725725

C) 720720

D) 21502150

E) 2750

OA is B
What is the best method to solve this? An Expert contribution will be appreciated. Thanks

Hi Roland2rule,
Let's take a look at your question.

Total people = 2500
35% people invest in municipal bonds, therefore,
Number of people who invest in municipal bonds = 2500 * 35/100 = 875

Number of people who invest in oil stocks = 2500*18/100 = 450
Number of people who do not invest in oil stocks = 2500 - 450 = 2050

The number of people who invest in both municipal bonds and oil stocks = 2500 * 7/100 = 175

Let's write all this information in a two way table.
$$ \text{ Oil Not Oil Total}$$
$$ \text{Municipal 175 700 875}$$
$$ \text{Not Municipal 275 1350 1625}$$
$$ \text{Total 450 2050 2500}$$
We need to find the probability that the person selected will be one who invests in municipal bonds and NOT in oils stocks.
We can see in the table that there are 700 people who invest in municipal bonds and NOT in oils stocks.

Therefore,
P(selecting a person who invest in municipal bonds and NOT in oils stocks) = 700/2500 = 7/25

Therefore, Option B is correct.

Hope this helps.
I am available if you'd like any follow up.

GMAT Prep From The Economist
We offer 70+ point score improvement money back guarantee.
Our average student improves 98 points.

Quote

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

by GMATGuruNY » Sun Jan 21, 2018 4:11 am

The answer choices should appear as follows:

Among a group of 2,500 people, 35 percent invest in municipal bonds, 18 percent invest in oil stocks, and 7 percent invest in both municipal bonds and oil stocks. If 1 person is to be randomly selected from the 2,500 people, what is the probability that the person selected will be one who invests in municipal bonds but NOT in oil stocks?

(A) 9/50
(B) 7/25
(C) 7/20
(D) 21/50
(E) 27/50

This is an EITHER/OR problem.
Everyone invests EITHER in stocks OR not in stocks.
Everyone invests EITHER in bonds OR not in bonds.
To organize the data in an either/or problem, use a DOUBLE-MATRIX.
Let S = stocks, NS = not stocks, B = bonds, NB = not bonds.
The following matrix is yielded:

Since the answer choices are FRACTIONS, the total number of people can be ANY VALUE.
Let the total number of people = 100:

35 percent invest in municipal bonds.
18 percent invest in oil stocks.
The following matrix is yielded:

7 percent invest in both municipal bonds and oil stocks.
The following matrix is yielded:

What is the probability that the person selected will be one who invests in municipal bonds and NOT in oils stocks?
(bonds but not stocks)/(total) = 28/100 = 7/25.

The correct answer is B.

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

Quote

GMAT/MBA Expert

Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pm; Location: Vancouver, BC; Thanked: 5254 times; Followed by:1268 members; GMAT Score:770

by Brent@GMATPrepNow » Sun Jan 21, 2018 8:59 am

Brent Hanneson - Creator of GMATPrepNow.com

Quote

Jeff@TargetTestPrep: GMAT Instructor; Posts: 1462; Joined: Thu Apr 09, 2015 9:34 am; Location: New York, NY; Thanked: 39 times; Followed by:22 members

hi

by Jeff@TargetTestPrep » Tue Jan 23, 2018 9:17 am

Roland2rule wrote:Among a group of 2,500 people, 35 percent invest in municipal bonds, 18 percent invest in oil stocks, and 7 percent invest in both municipal bonds and oil stocks. If 1 person is to be randomly selected from the 2,500 people, what is the probability that the person selected will be one who invests in municipal bonds and NOT in oils stocks?

A) 9/50

B) 7/25

C) 7/20

D) 21/50

E) 27/50

The number of people who invest in ONLY municipal bonds is:

2,500 x 0.35 - 2,500 x 0.07

2,500(0.35 - 0.07) = 2,500(0.28) = 700

So, the probability that the person selected will be one who invests in municipal bonds and NOT in oils stocks is 700/2500 = 7/25

Answer: B

Jeffrey Miller
Head of GMAT Instruction
[email protected]