Probability involving 'EITHER OR'

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dtweah: Master | Next Rank: 500 Posts; Posts: 487; Joined: Fri Mar 27, 2009 5:49 am; Thanked: 36 times

by dtweah » Sat Aug 14, 2010 3:08 pm

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In a town of 3000 people, 600 are over 50 years old and 1000 are female. It is known that 30% of the female are over 50 years. What is the probability that the person chosen at random is either a female or over 50 years?

A. 11:13

B. 13:17

C. 2:3

D. 9:17

E. 13:9

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Source: Beat The GMAT — Problem Solving | Sat Aug 14, 2010 3:08 pm

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Ian Stewart: GMAT Instructor; Posts: 2623; Joined: Mon Jun 02, 2008 3:17 amFollowed by: 355 members; Location: Montreal; Thanked: 1090 times; GMAT Score:780

by Ian Stewart » Sat Aug 14, 2010 11:51 pm

dtweah wrote:In a town of 3000 people, 600 are over 50 years old and 1000 are female. It is known that 30% of the female are over 50 years. What is the probability that the person chosen at random is either a female or over 50 years?

A. 11:13

B. 13:17

C. 2:3

D. 9:17

E. 13:9

[spoiler]https://www.greguide.com/Free-GRE-Practi ... est-5.html[/spoiler]

The correct answer isn't there. The answer choices are expressed in terms of what are known as 'odds' (the ratio of good outcomes to bad ones). A probability is the ratio of good outcomes to *all* outcomes, and thus is always between 0 and 1.

Here we have 1000 women, 30% of whom are over fifty years old, so we have 300 women over fifty. We must therefore have 300 men over fifty. Adding these 300 over-fifty men to the 1000 women, there are thus 1300 people who are either female or over fifty, and the probability of selecting such a person is 1300/3000 = 13/30.

I'm sure B is *intended* to be the correct answer here, but it is not written correctly. It's a dodgy question.

For online GMAT math tutoring, or to buy my higher-level Quant books and problem sets, contact me at ianstewartgmat at gmail.com

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dtweah: Master | Next Rank: 500 Posts; Posts: 487; Joined: Fri Mar 27, 2009 5:49 am; Thanked: 36 times

by dtweah » Sun Aug 15, 2010 4:08 am

Ian Stewart wrote:
dtweah wrote:In a town of 3000 people, 600 are over 50 years old and 1000 are female. It is known that 30% of the female are over 50 years. What is the probability that the person chosen at random is either a female or over 50 years?

A. 11:13

B. 13:17

C. 2:3

D. 9:17

E. 13:9

[spoiler]https://www.greguide.com/Free-GRE-Practi ... est-5.html[/spoiler]
The correct answer isn't there. The answer choices are expressed in terms of what are known as 'odds' (the ratio of good outcomes to bad ones). A probability is the ratio of good outcomes to *all* outcomes, and thus is always between 0 and 1.

Here we have 1000 women, 30% of whom are over fifty years old, so we have 300 women over fifty. We must therefore have 300 men over fifty. Adding these 300 over-fifty men to the 1000 women, there are thus 1300 people who are either female or over fifty, and the probability of selecting such a person is 1300/3000 = 13/30.

I'm sure B is *intended* to be the correct answer here, but it is not written correctly. It's a dodgy question.

Yep Ian I got 13/30 as well and tried to email them about b being wrong.

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Gurpinder: Legendary Member; Posts: 659; Joined: Mon Dec 14, 2009 8:12 amFollowed by: 3 members; Thanked: 32 times

by Gurpinder » Sun Aug 15, 2010 11:38 am

Ian Stewart wrote:
The correct answer isn't there. The answer choices are expressed in terms of what are known as 'odds' (the ratio of good outcomes to bad ones). A probability is the ratio of good outcomes to *all* outcomes, and thus is always between 0 and 1.

Here we have 1000 women, 30% of whom are over fifty years old, so we have 300 women over fifty. We must therefore have 300 men over fifty. Adding these 300 over-fifty men to the 1000 women, there are thus 1300 people who are either female or over fifty, and the probability of selecting such a person is 1300/3000 = 13/30.

I'm sure B is *intended* to be the correct answer here, but it is not written correctly. It's a dodgy question.

Hey Ian,

I don't know why I got 19/30. Oh and, where did you get that 300 men over 50 from.

The way I did it was and please tell me what I am doing wrong:

3000 people
(1) 600 are 50+
(2) 1000 females. > 300 are 50+.

Therefore: 1000/3000 + 900/3000 = 19/30.

Thanks,

"Do not confuse motion and progress. A rocking horse keeps moving but does not make any progress."
- Alfred A. Montapert, Philosopher.

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Ian Stewart: GMAT Instructor; Posts: 2623; Joined: Mon Jun 02, 2008 3:17 amFollowed by: 355 members; Location: Montreal; Thanked: 1090 times; GMAT Score:780

by Ian Stewart » Sun Aug 15, 2010 12:36 pm

Gurpinder wrote: I don't know why I got 19/30. Oh and, where did you get that 300 men over 50 from.

The way I did it was and please tell me what I am doing wrong:

3000 people
(1) 600 are 50+
(2) 1000 females. > 300 are 50+.

The 300 females who are 50+ are *part* of the group of 600 who are 50+. So we have 300 women and 300 men who are 50+. We then have 700 other women who are younger than 50. Adding those numbers gives us our 1300 people.

For online GMAT math tutoring, or to buy my higher-level Quant books and problem sets, contact me at ianstewartgmat at gmail.com

ianstewartgmat.com

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Bitesizebabe: Newbie | Next Rank: 10 Posts; Posts: 1; Joined: Wed May 04, 2016 10:04 am

by Bitesizebabe » Wed May 04, 2016 10:39 am

Hi ! So this question really annoyed me because I thought the same thing: the answer isn't provided. But.....

Either or probability considers one or the other, not one out of the total. So...

We begin with the 1,000 women, where 300 are over 50 yrs. That means that 300 men are also over 50 yrs. Without double counting those 300 women, we add the 300 men to the thousand women and get 1,300.

1,300 is the number of those that are either 50 yrs+ OR a woman of to be selected out of random. Here's the catch.

A ratio is to compare what is to what is not. So...

3,000 - 1,300 = 1,700

Reduced, we have 13:17 (those who are:those who are not)

I hope that break down makes sense !

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