 It is currently 21 Aug 2019, 08:07 ### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here. # QOTD # 17 Of the 40 specimens of bacteria in a dish, 3 speci  Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:
Founder  Joined: 18 Apr 2015
Posts: 7741
Followers: 143

Kudos [?]: 1593 , given: 7032

QOTD # 17 Of the 40 specimens of bacteria in a dish, 3 speci [#permalink]
Expert's post 00:00

Question Stats: 58% (01:27) correct 41% (01:56) wrong based on 17 sessions
Of the 40 specimens of bacteria in a dish, 3 specimens have a certain trait. If 5 specimens are to be selected from the dish at random and without replacement, which of the following represents the probability that only 1 of the 5 specimens selected will have the trait?

A) $$\frac{\frac{5}{1}}{\frac{40}{3}}=$$

B) $$\frac{\frac{5}{1}}{\frac{40}{5}}=$$

C) $$\frac{\frac{40}{3}}{\frac{40}{5}}=$$

D) $$\frac{\frac{3}{1} \times \frac{37}{4}}{\frac{40}{3}}=$$

E)$$\frac{\frac{3}{1} \times \frac{37}{4}}{\frac{40}{5}}=$$

Practice Questions
Question: 17
Page: 180
[Reveal] Spoiler: OA

_________________
Founder  Joined: 18 Apr 2015
Posts: 7741
Followers: 143

Kudos [?]: 1593 , given: 7032

Re: QOTD # 17 Of the 40 specimens of bacteria in a dish, 3 speci [#permalink]
Expert's post
Explanation

A question like this is much better to go step by step, dividing it into chunks.

Now, we said that we have to select 1 specimens among five BUT only 3 over 40 have such traits.

To select 5 among 40 is, the total possibilities, $$\frac{40}{5}$$ in the denominator

In the numerator, we have 1 specimens among 3 and then select 4 among 37 that do not have the traits.

[m]\frac{\frac{3}{1} \times \frac{37}{4}}{\frac{40}{5}}

The best answer is E
_________________
Intern Joined: 06 Aug 2017
Posts: 1
Followers: 0

Kudos [?]: 0 , given: 0

Re: QOTD # 17 Of the 40 specimens of bacteria in a dish, 3 speci [#permalink]
I couldn't understand the solution properly.why we take 37C4??? Is that another way to solve this math ???
Founder  Joined: 18 Apr 2015
Posts: 7741
Followers: 143

Kudos [?]: 1593 , given: 7032

Re: QOTD # 17 Of the 40 specimens of bacteria in a dish, 3 speci [#permalink]
Expert's post
The probability that only 1 of the 5 specimens selected from the 40 specimens will have the trait is equal to

$$\frac{numbers of way to select 5 specimens, only 1 of which has the traits}{numbers of ways to select 5 specimens}$$

The number of ways 5 specimens can be selected from the 40 specimens is $$\frac{40}{5}$$.To select 5 specimens, only 1 of which has the trait, you have to select 1 of the 3 specimens that have the trait and select 4 of the 37 specimens that do not have the trait. The number of such selections is the product $$\frac{3}{1}$$ * $$\frac{37}{4}$$.

So the probability that only 1 of the 5 specimens selected will have the trait is represented by $$\frac{3}{1}$$ * $$\frac{37}{4}$$ / $$\frac{40}{5}$$

E is the best
_________________
Manager  Joined: 01 Nov 2018
Posts: 87
Followers: 0

Kudos [?]: 45 , given: 22

Re: QOTD # 17 Of the 40 specimens of bacteria in a dish, 3 speci [#permalink]
Expert's post
Carcass wrote:
The probability that only 1 of the 5 specimens selected from the 40 specimens will have the trait is equal to

$$\frac{numbers of way to select 5 specimens, only 1 of which has the traits}{numbers of ways to select 5 specimens}$$

The number of ways 5 specimens can be selected from the 40 specimens is $$\frac{40}{5}$$.To select 5 specimens, only 1 of which has the trait, you have to select 1 of the 3 specimens that have the trait and select 4 of the 37 specimens that do not have the trait. The number of such selections is the product $$\frac{3}{1}$$ * $$\frac{37}{4}$$.

So the probability that only 1 of the 5 specimens selected will have the trait is represented by $$\frac{3}{1}$$ * $$\frac{37}{4}$$ / $$\frac{40}{5}$$

E is the best

I dont mean to correct a pro, but E is impossible. if you calculate E. that total is 3.46.... We are looking for a probability here, which has to be less than 1 Manager  Joined: 01 Nov 2018
Posts: 87
Followers: 0

Kudos [?]: 45  , given: 22

Re: QOTD # 17 Of the 40 specimens of bacteria in a dish, 3 speci [#permalink]
1
This post received
KUDOS
Expert's post
Lets break it down muuuuch more simply.

First way is...
the total number of combinations is going to be 40C5 which is 40!/(5!35!). this will be your denominator
The total number of ways to pick one specimen with the desired train is 3C1, which is just 3,
The total number of ways to pick four specimen without the desired train is 37C4
Now the question is asking what are the chances of picking a specimen with the certain trait,
you just multiply 3*37C4, then divide that product by 40C5
3*37C4/(40C5)

which is (3*(37!/4!33!)/(40!/5!35!)
Founder  Joined: 18 Apr 2015
Posts: 7741
Followers: 143

Kudos [?]: 1593 , given: 7032

Re: QOTD # 17 Of the 40 specimens of bacteria in a dish, 3 speci [#permalink]
Expert's post
Maybe the OA in the Official Quant Reasoning is wrong.

However, as per the book , it is E
_________________
Director Joined: 09 Nov 2018
Posts: 509
Followers: 0

Kudos [?]: 39 , given: 1

Re: QOTD # 17 Of the 40 specimens of bacteria in a dish, 3 speci [#permalink]
Carcass wrote:
Maybe the OA in the Official Quant Reasoning is wrong.

However, as per the book , it is E

No, the OA is perfectly all right. There is typos in the answers here.

For example for choice e,
In instead of $$\frac{\frac{3}{1} * \frac{37}{4}}{\frac{40}{5}}=$$,

It should be $$\frac{3C1 * 37C4}{40C5}=$$

It is the correct answer.
Founder  Joined: 18 Apr 2015
Posts: 7741
Followers: 143

Kudos [?]: 1593 , given: 7032

Re: QOTD # 17 Of the 40 specimens of bacteria in a dish, 3 speci [#permalink]
Expert's post
No typo in the answer choices provided by the Offical Quantitative Reasoning Book

Attachment: shot35.jpg [ 17.18 KiB | Viewed 1767 times ]

_________________
Manager Joined: 08 Dec 2018
Posts: 94
Followers: 0

Kudos [?]: 34 , given: 30

Re: QOTD # 17 Of the 40 specimens of bacteria in a dish, 3 speci [#permalink]
Carcass wrote:
No typo in the answer choices provided by the Offical Quantitative Reasoning Book

Attachment:
shot35.jpg

Does the format used in the official book IS the same as it has been used in the explanation ( on this forum, i.e. Numerator /Denominator form)??
Founder  Joined: 18 Apr 2015
Posts: 7741
Followers: 143

Kudos [?]: 1593 , given: 7032

Re: QOTD # 17 Of the 40 specimens of bacteria in a dish, 3 speci [#permalink]
Expert's post
As AE pointed out, the answer should be in the format

$$\frac{3C1 * 37C4}{40C5}=$$

Regards
_________________ Re: QOTD # 17 Of the 40 specimens of bacteria in a dish, 3 speci   [#permalink] 19 Mar 2019, 23:34
Display posts from previous: Sort by

# QOTD # 17 Of the 40 specimens of bacteria in a dish, 3 speci  Question banks Downloads My Bookmarks Reviews Important topics Powered by phpBB © phpBB Group Kindly note that the GRE® test is a registered trademark of the Educational Testing Service®, and this site has neither been reviewed nor endorsed by ETS®.