NEW HERE? LEARN MORE
closeclose
Last visit was: 26 Apr 2024, 09:36 It is currently 26 Apr 2024, 09:36
Decision Tracker
My Rewards
New posts
New comers' posts

Close
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.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel

James, Kara and Smith are three friends who have applied for a job at

SORT BY:
Date
Kudos
Tags:
Find Similar Topics 
Show Tags
Hide Tags
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 92945
Own Kudos [?]: 619197 [21]
Given Kudos: 81609
Send PM
CAT Tests Forum Quiz Mode
James, Kara and Smith are three friends who have applied for a job at [#permalink] New post   02 Jun 2020, 08:33
21
Bookmarks
Expert Reply
00:00
A
B
C
D
E

Difficulty:

65% (hard)

Question Stats:

59% (02:43) correct 41% (02:15) wrong based on 117 sessions
Hide Show timer Statistics
James, Kara and Smith are three friends who have applied for a job at Company X. Their probabilities of getting selected for interview are 2/5, 1/3 and 4/7 respectively. If Company X offers a job to only 25% of the applicants it interviews, what is the probability that only Kara receives a job offer out of the three friends?

A. 1/12
B. 9/140
C. 1/42
D. 27/2240
E. 2/175
ShowHide Answer
Official Answer
B
Most Helpful Reply
User avatar
L
BrentGMATPrepNow
GMAT Club Legend
GMAT Club Legend
Joined: 12 Sep 2015
Posts: 6818
Own Kudos [?]: 29939 [6]
Given Kudos: 799
Location: Canada
Send PM
Re: James, Kara and Smith are three friends who have applied for a job at [#permalink] New post   02 Jun 2020, 09:15
4
Kudos
2
Bookmarks
Expert Reply
Top Contributor
Bunuel wrote:
James, Kara and Smith are three friends who have applied for a job at Company X. Their probabilities of getting selected for interview are 2/5, 1/3 and 4/7 respectively. If Company X offers a job to only 25% of the applicants it interviews, what is the probability that only Kara receives a job offer out of the three friends?

A. 1/12
B. 9/140
C. 1/42
D. 27/2240
E. 2/175


P(only Kara gets offer) = P(Kara gets job offer AND James gets NO job offer AND Smith gets NO job offer)
= P(Kara gets job offer) x P(James gets NO job offer) x P(Smith gets NO job offer)

Let's calculate each probability separately:

P(Kara gets job offer)
P(Kara gets job offer) = P(gets interview AND receives job offer)
= P(gets interview) x P(receives job offer)
= 1/3 x 1/4 (since the company offers a job to only 25% of interviewees)
= 1/12

P(James gets NO job offer)
P(James gets NO job offer) = P(gets interview AND receives NO job offer OR doesn't get interview)
= P(gets interview) x P(receives NO job offer) + P(doesn't get interview)
= (2/5 x 3/4) + 3/5
= 3/10 + 3/5
= 9/10

P(Smith gets NO job offer)
P(Smith gets NO job offer) = P(gets interview AND receives NO job offer OR doesn't get interview)
= P(gets interview) x P(receives NO job offer) + P(doesn't get interview)
= (4/7 x 3/4) + 3/7
= 3/7 + 3/7
= 6/7

So.....
P(only Kara gets offer) = P(Kara gets job offer) x P(James gets NO job offer) x P(Smith gets NO job offer)
= 1/12 x 9/10 x 6/7
= 54/840
= 9/140

Answer: B

Cheers,
Brent
General Discussion
User avatar
L
Archit3110
GMAT Club Legend
GMAT Club Legend
Joined: 18 Aug 2017
Status:You learn more from failure than from success.
Posts: 8020
Own Kudos [?]: 4098 [2]
Given Kudos: 242
Location: India
Concentration: Sustainability, Marketing
GMAT Focus 1:
545 Q79 V79 DI73
GPA: 4
WE:Marketing (Energy and Utilities)
Send PM
GMAT ToolKit User CAT Tests
Re: James, Kara and Smith are three friends who have applied for a job at [#permalink] New post   02 Jun 2020, 09:00
1
Kudos
1
Bookmarks
Given P of getting Job J = 2/5 ; K = 1/3 and S= 4/7
and not getting job J = 3/5 ; K = 2/3 and S = 3/7
and 25% or say 1/4 will get a Job
so the probability that only Kara receives a job offer out of the three friends
we have ; 1/4 * 3c1 * ( 1/3 * 3/5 * 3/7)
=> 3/140 *3c1 ; 9/140
OPTION B


Bunuel wrote:
James, Kara and Smith are three friends who have applied for a job at Company X. Their probabilities of getting selected for interview are 2/5, 1/3 and 4/7 respectively. If Company X offers a job to only 25% of the applicants it interviews, what is the probability that only Kara receives a job offer out of the three friends?

A. 1/12
B. 9/140
C. 1/42
D. 27/2240
E. 2/175
User avatar
G
NitishJain
IESE School Moderator
Joined: 11 Feb 2019
Posts: 271
Own Kudos [?]: 171 [2]
Given Kudos: 53
Send PM
Re: James, Kara and Smith are three friends who have applied for a job at [#permalink] New post   02 Jun 2020, 12:51
1
Bookmarks
IMO B

Probability of only Kara getting selected = (Probability of Kara getting selected for an interview * Probability of Kara getting selected for a job) *
(1- Probability of James getting selected for an interview * Probability of James getting selected for a job) *
(1- Probability of Smith getting selected for an interview * Probability of Smith getting selected for a job)


= (1/3 * 1/4) (1 - 2/5 * 1/4) (1 - 4/7* 1/4) = 1/3 * 1/4 * 9/10 * 6/7 = 9/140
User avatar
G
rishab0507
Manager
Manager
Joined: 12 Mar 2019
Posts: 191
Own Kudos [?]: 104 [0]
Given Kudos: 105
Send PM
Re: James, Kara and Smith are three friends who have applied for a job at [#permalink] New post   02 Jun 2020, 12:54
Archit3110 wrote:
Given P of getting Job J = 2/5 ; K = 1/3 and S= 4/7
and not getting job J = 3/5 ; K = 2/3 and S = 3/7
and 25% or say 1/4 will get a Job
so the probability that only Kara receives a job offer out of the three friends
we have ; 1/4 * 3c1 * ( 1/3 * 3/5 * 3/7)
=> 3/140 *3c1 ; 9/140
OPTION B


Bunuel wrote:
James, Kara and Smith are three friends who have applied for a job at Company X. Their probabilities of getting selected for interview are 2/5, 1/3 and 4/7 respectively. If Company X offers a job to only 25% of the applicants it interviews, what is the probability that only Kara receives a job offer out of the three friends?

A. 1/12
B. 9/140
C. 1/42
D. 27/2240
E. 2/175


why multiplied by 3c1 ? I did rest calc, getting 3/140, missed 3c1 multiplication, can u help
User avatar
L
ScottTargetTestPrep
Target Test Prep Representative
Joined: 14 Oct 2015
Status:Founder & CEO
Affiliations: Target Test Prep
Posts: 18763
Own Kudos [?]: 22056 [1]
Given Kudos: 283
Location: United States (CA)
Send PM
Re: James, Kara and Smith are three friends who have applied for a job at [#permalink] New post   06 Jun 2020, 05:27
1
Kudos
Expert Reply
Bunuel wrote:
James, Kara and Smith are three friends who have applied for a job at Company X. Their probabilities of getting selected for interview are 2/5, 1/3 and 4/7 respectively. If Company X offers a job to only 25% of the applicants it interviews, what is the probability that only Kara receives a job offer out of the three friends?

A. 1/12
B. 9/140
C. 1/42
D. 27/2240
E. 2/175


Solution:

The probability that only Kara receives a job offer out of the three friends is the probability that Kara receives a job offer AND James does not receive a job offer AND Smith does not receive a job offer. Because we use the word “and,” we will use the multiplication rule.

P(only Kara receives a job offer) = P(Kara receives a job offer) x P(James does not receive a job offer) x P(Smith does not receive a job offer)

Now let’s determine the probability of each.

P(Kara receives a job offer) = P(she gets an interview) x P(she gets the job offer, given that she’s gotten an interview) = 1/3 x 1/4 = 1/12

P(James does not receive a job offer) = P(he does not get an interview) + P(he gets an interview) x P(he doesn’t get the job offer given that he’s gotten an interview) = 3/5 + 2/5 x 3/4 = 3/5 + 3/10 = 9/10

P(Smith does not receive a job offer) = P(he does not get an interview) + P(he gets an interview) x P(he doesn’t get the job offer given that he’s gotten an interview) = 3/7 + 4/7 x 3/4 = 3/7 + 3/7 = 6/7

Therefore,

P(only Kara receives a job offer) = 1/12 x 9/10 x 6/7 = 1/2 x 9/10 x 1/7 = 9/140

Answer: B
User avatar
B
gmattyfatty
Intern
Intern
Joined: 12 Mar 2023
Posts: 34
Own Kudos [?]: 4 [0]
Given Kudos: 11
Send PM
James, Kara and Smith are three friends who have applied for a job at [#permalink] New post   27 Apr 2023, 22:33
I eventually got this correct but i'm a bit confused. For this question we solve doing the following

P(Karen only) = P(Karen) * P(Not James) * P(Not Smith)

but after doing this slightly similar question
https://gmatclub.com/forum/there-is-a-5 ... 47886.html

I thought we are supposed to solve it as such:
P(Karen) = 1 - (P(All 3) + P(Only James) + P(Only Smith) + P(James and Smith) + P(Karen and Jame) + P(Karen and Smith) + P(None))

ScottTargetTestPrep is there something I'm missing about how to structure the equation, or when to use one method vs the other?
GMAT Club Bot
gmatclubot
James, Kara and Smith are three friends who have applied for a job at [#permalink]
27 Apr 2023, 22:33
Moderators:
Bunuel
Math Expert
92945 posts
yashikaaggarwal
Senior Moderator - Masters Forum
3137 posts

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne
Main navigation
GMAT Resources
Partners
MBA Resources
www.gmac.com|www.mba.com | | GMAT Club Rules | Terms and Conditions