NEW HERE? LEARN MORE
closeclose
Last visit was: 23 Apr 2024, 13:52 It is currently 23 Apr 2024, 13:52
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

A certain class consists of 8 students, including Kim. Each day, three

SORT BY:
Date
Kudos
Tags:
Find Similar Topics 
Show Tags
Hide Tags
User avatar
metallicafan
Retired Moderator
Joined: 04 Oct 2009
Status:2000 posts! I don't know whether I should feel great or sad about it! LOL
Posts: 767
Own Kudos [?]: 3944 [57]
Given Kudos: 109
Location: Peru
Concentration: Finance, SMEs, Developing countries, Public sector and non profit organizations
Schools:Harvard, Stanford, Wharton, MIT & HKS (Government)
GPA: 4.0
WE 1: Economic research
WE 2: Banking
WE 3: Government: Foreign Trade and SMEs
Send PM
A certain class consists of 8 students, including Kim. Each day, three [#permalink] New post   17 Feb 2012, 07:50
2
Kudos
55
Bookmarks
00:00
A
B
C
D
E

Difficulty:

25% (medium)

Question Stats:

75% (01:33) correct 25% (02:02) wrong based on 966 sessions
Hide Show timer Statistics
A certain class consists of 8 students, including Kim. Each day, three tasks must be completed and are assigned as follows: one of the 8 students is selected at random to complete Task A, one of the remaining 7 students is selected at random to complete Task B, and one of the remaining six students is selected at random to complete Task C. What is the probability that Kim will be selected to complete one of the three tasks?

(A) 1/3
(B) 3/8
(C) 1/24
(D) 1/336
(E) 1/512

Show Spoiler
In solved in this way:

Probability of completing Task A:

\(\frac{1}{8} * \frac{7}{7} * \frac{6}{6} = \frac{1}{8}\)

Probability of completing Task B:

\(\frac{7}{8} * \frac{1}{7} * \frac{6}{6} = \frac{1}{8}\)

Probability of completing Task C:

\(\frac{7}{8} * \frac{6}{7} * \frac{1}{6} = \frac{1}{8}\)

Therefore: \(\frac{1}{8} + \frac{1}{8} + \frac{1}{8} = [m]\frac{3}{8}\)[/m]

Is there another way to solve it faster?

Source: Jeff Sackman questions - https://www.gmathacks.com
ShowHide Answer
Official Answer
B
Most Helpful Reply
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 92883
Own Kudos [?]: 618584 [23]
Given Kudos: 81563
Send PM
CAT Tests Forum Quiz Mode
Re: A certain class consists of 8 students, including Kim. Each day, three [#permalink] New post   17 Feb 2012, 08:23
11
Kudos
12
Bookmarks
Expert Reply
metallicafan wrote:
Bunuel wrote:
metallicafan wrote:
A certain class consists of 8 students, including Kim. Each day, three tasks must be completed and are assigned as follows: one of the 8 students is selected at random to complete Task A, one of the remaining 7 students is selected at random to complete Task B, and one of the remaining six students is selected at random to complete Task C. What is the probability that Kim will be selected to complete one of the three tasks?


Since there are total of 8 students and we are selecting 3 of them, then the probability that Kim will be selected is simply 3/8 (she has 3 chances out of 8).

P.S. Please provide answer choices if available.


Thank you bunuel! However, I don't get your approach well. Could you explain your logic? I believe that the probability of picking somenone in the second task is different from picking someone in the first because the number of elements available to pick changes. That's why my approach is step by step.
Please, show me the light!


The wording of the question makes it harder then it is. The question basically asks: what is the probability that Kim is among the first 3 students out of 8, which is 3/8.

One can also do: \(P=\frac{C^1_1*C^2_7}{C^3_8}=\frac{3}{8}\), where \(C^1_1\) is # of ways to select Kim, \(C^2_7\) is # of ways to select any 2 students out of 7 left and \(C^3_8\) is total # of ways to select 3 students from 8;

Or: you can find the probability that among 3 students selected to complete the tasks there won't be Kim and subtract it from 1:
\(P=1-\frac{C^3_7}{C^3_8}=\frac{3}{8}\);

Or: the same with probability approach: \(P=1-\frac{7}{8}*\frac{6}{7}*\frac{5}{6}=\frac{3}{8}\).

As you can see first approach is easiest and shortest one.

P.S. What about the answer choices?
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 92883
Own Kudos [?]: 618584 [8]
Given Kudos: 81563
Send PM
CAT Tests Forum Quiz Mode
Re: A certain class consists of 8 students, including Kim. Each day, three [#permalink] New post   17 Feb 2012, 07:55
5
Kudos
3
Bookmarks
Expert Reply
metallicafan wrote:
A certain class consists of 8 students, including Kim. Each day, three tasks must be completed and are assigned as follows: one of the 8 students is selected at random to complete Task A, one of the remaining 7 students is selected at random to complete Task B, and one of the remaining six students is selected at random to complete Task C. What is the probability that Kim will be selected to complete one of the three tasks?


Since there are total of 8 students and we are selecting 3 of them, then the probability that Kim will be selected is simply 3/8 (she has 3 chances out of 8).

P.S. Please provide answer choices if available.
General Discussion
User avatar
metallicafan
Retired Moderator
Joined: 04 Oct 2009
Status:2000 posts! I don't know whether I should feel great or sad about it! LOL
Posts: 767
Own Kudos [?]: 3944 [0]
Given Kudos: 109
Location: Peru
Concentration: Finance, SMEs, Developing countries, Public sector and non profit organizations
Schools:Harvard, Stanford, Wharton, MIT & HKS (Government)
GPA: 4.0
WE 1: Economic research
WE 2: Banking
WE 3: Government: Foreign Trade and SMEs
Send PM
Re: A certain class consists of 8 students, including Kim. Each day, three [#permalink] New post   17 Feb 2012, 08:12
Bunuel wrote:
metallicafan wrote:
A certain class consists of 8 students, including Kim. Each day, three tasks must be completed and are assigned as follows: one of the 8 students is selected at random to complete Task A, one of the remaining 7 students is selected at random to complete Task B, and one of the remaining six students is selected at random to complete Task C. What is the probability that Kim will be selected to complete one of the three tasks?


Since there are total of 8 students and we are selecting 3 of them, then the probability that Kim will be selected is simply 3/8 (she has 3 chances out of 8).

P.S. Please provide answer choices if available.


Thank you bunuel! However, I don't get your approach well. Could you explain your logic? I believe that the probability of picking somenone in the second task is different from picking someone in the first because the number of elements available to pick changes. That's why my approach is step by step.
Please, show me the light!
User avatar
metallicafan
Retired Moderator
Joined: 04 Oct 2009
Status:2000 posts! I don't know whether I should feel great or sad about it! LOL
Posts: 767
Own Kudos [?]: 3944 [0]
Given Kudos: 109
Location: Peru
Concentration: Finance, SMEs, Developing countries, Public sector and non profit organizations
Schools:Harvard, Stanford, Wharton, MIT & HKS (Government)
GPA: 4.0
WE 1: Economic research
WE 2: Banking
WE 3: Government: Foreign Trade and SMEs
Send PM
Re: A certain class consists of 8 students, including Kim. Each day, three [#permalink] New post   17 Feb 2012, 08:49
Thank you Bunuel!, I have updated the post with the choices. 8-)
User avatar
pratikbais
Intern
Intern
Joined: 10 Feb 2012
Posts: 33
Own Kudos [?]: 327 [0]
Given Kudos: 41
Location: India
Concentration: Marketing, Strategy
GMAT 1: 640 Q48 V31
GPA: 3.45
WE:Marketing (Pharmaceuticals and Biotech)
Send PM
Re: A certain class consists of 8 students, including Kim. Each day, three [#permalink] New post   17 Feb 2012, 10:00
Thankx Bunuel, the explanation covers all possible ways of solving the problem
avatar
Gwydion
Intern
Intern
Joined: 17 Aug 2011
Posts: 20
Own Kudos [?]: 28 [5]
Given Kudos: 2
Schools: HBS '15 (D) Kellogg '15 (A) Wharton '15 (WL) Stanford '15 (D) LBS '14 (M)
GMAT 1: 750 Q48 V44
GPA: 3.8
WE:Management Consulting (Consulting)
Send PM
Re: A certain class consists of 8 students, including Kim. Each day, three [#permalink] New post   17 Feb 2012, 17:43
4
Kudos
1
Bookmarks
One more way to sove this is to reverse the logic:
NOT chosen on first, second and third pick leads to the following calculation:
7/8 * 6/7 * 5/6 = 0,625. Since we are looking for the probability Kim gets chosen it's 1-0,625 = 0,375 = 3/8
avatar
Bowtie
Intern
Intern
Joined: 08 Sep 2011
Posts: 29
Own Kudos [?]: 23 [5]
Given Kudos: 5
Concentration: Finance, Strategy
Send PM
Re: A certain class consists of 8 students, including Kim. Each day, three [#permalink] New post   23 Feb 2012, 10:06
4
Kudos
1
Bookmarks
I agree with B 3/8

first task = 1/8 chance

second task= 7/8*1/7 = 1/8

third task = 7/8*6/7*1/6 = 1/8

chance that she gets picked for one of these is 1/8+1/8+1/8 or 3/8
avatar
msharmita
Intern
Intern
Joined: 26 Jan 2013
Posts: 7
Own Kudos [?]: 5 [2]
Given Kudos: 1
Concentration: Marketing, Strategy
Schools: ISB '15 PGDM (GM) '15 Kellogg 1YR '15 HEC '15
GMAT Date: 10-11-2014
Send PM
Re: A certain class consists of 8 students, including Kim. Each day, three [#permalink] New post   03 May 2014, 23:35
1
Kudos
1
Bookmarks
metallicafan wrote:
A certain class consists of 8 students, including Kim. Each day, three tasks must be completed and are assigned as follows: one of the 8 students is selected at random to complete Task A, one of the remaining 7 students is selected at random to complete Task B, and one of the remaining six students is selected at random to complete Task C. What is the probability that Kim will be selected to complete one of the three tasks?
(A) 1/3
(B) 3/8
(C) 1/24
(D) 1/336
(E) 1/512

In solved in this way:

Probability of completing Task A:

\(\frac{1}{8} * \frac{7}{7} * \frac{6}{6} = \frac{1}{8}\)

Probability of completing Task B:

\(\frac{7}{8} * \frac{1}{7} * \frac{6}{6} = \frac{1}{8}\)

Probability of completing Task C:

\(\frac{7}{8} * \frac{6}{7} * \frac{1}{6} = \frac{1}{8}\)

Therefore: \(\frac{1}{8} + \frac{1}{8} + \frac{1}{8} = [m]\frac{3}{8}\)[/m]

Is there another way to solve it faster?

Source: Jeff Sackman questions - https://www.gmathacks.com



Hello,

Can someone please explain :
for completion of task B - why 7/8 * 1/7* 6/6??

for completion of task C - why 7/8 * 6/7* 1/6??

plx explain the one in BOLD especially..

Sharmita
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 92883
Own Kudos [?]: 618584 [4]
Given Kudos: 81563
Send PM
CAT Tests Forum Quiz Mode
Re: A certain class consists of 8 students, including Kim. Each day, three [#permalink] New post   04 May 2014, 03:01
4
Bookmarks
Expert Reply
msharmita wrote:
metallicafan wrote:
A certain class consists of 8 students, including Kim. Each day, three tasks must be completed and are assigned as follows: one of the 8 students is selected at random to complete Task A, one of the remaining 7 students is selected at random to complete Task B, and one of the remaining six students is selected at random to complete Task C. What is the probability that Kim will be selected to complete one of the three tasks?
(A) 1/3
(B) 3/8
(C) 1/24
(D) 1/336
(E) 1/512

In solved in this way:

Probability of completing Task A:

\(\frac{1}{8} * \frac{7}{7} * \frac{6}{6} = \frac{1}{8}\)

Probability of completing Task B:

\(\frac{7}{8} * \frac{1}{7} * \frac{6}{6} = \frac{1}{8}\)

Probability of completing Task C:

\(\frac{7}{8} * \frac{6}{7} * \frac{1}{6} = \frac{1}{8}\)

Therefore: \(\frac{1}{8} + \frac{1}{8} + \frac{1}{8} = [m]\frac{3}{8}\)[/m]

Is there another way to solve it faster?

Source: Jeff Sackman questions - https://www.gmathacks.com



Hello,

Can someone please explain :
for completion of task B - why 7/8 * 1/7* 6/6??

for completion of task C - why 7/8 * 6/7* 1/6??

plx explain the one in BOLD especially..

Sharmita


Probability of completing Task A:

P(Kim)*P(any)*P(any) = \(\frac{1}{8} * \frac{7}{7} * \frac{6}{6} = \frac{1}{8}\)

Probability of completing Task B:

P(any bu Kim)*P(Kim)*P(any) = \(\frac{7}{8} * \frac{1}{7} * \frac{6}{6} = \frac{1}{8}\)

Probability of completing Task C:

P(any but Kim)*P(any but Kim)*P(any) = \(\frac{7}{8} * \frac{6}{7} * \frac{1}{6} = \frac{1}{8}\)

Faster solutions are here: a-certain-class-consists-of-8-students-including-kim-127730.html#p1046004 and here: a-certain-class-consists-of-8-students-including-kim-127730.html#p1046020

Similar questions to practice:
a-box-contains-3-yellow-balls-and-5-black-balls-one-by-one-90272.html
a-bag-contains-3-white-balls-3-black-balls-2-red-balls-100023.html
each-of-four-different-locks-has-a-matching-key-the-keys-101553.html
if-40-people-get-the-chance-to-pick-a-card-from-a-canister-97015.html
new-set-of-mixed-questions-150204-100.html#p1208473
a-medical-researcher-must-choose-one-of-14-patients-to-recei-124775.html

Hope this helps.
avatar
lnreddy
Intern
Intern
Joined: 28 Jul 2016
Posts: 4
Own Kudos [?]: [0]
Given Kudos: 7
Send PM
Re: A certain class consists of 8 students, including Kim. Each day, three [#permalink] New post   24 Aug 2016, 08:46
Hi Bunuel,

Should the question be read as "What is the probability that Kim will be selected to complete ATLEAST one of the three tasks?"

Or should it be read as "What is the probability that Kim will be selected to complete EXACTLY one of the three tasks?"

I felt the question was slightly ambiguous. If so, will such type of questions appear on the GMAT ?
avatar
lnreddy
Intern
Intern
Joined: 28 Jul 2016
Posts: 4
Own Kudos [?]: [0]
Given Kudos: 7
Send PM
Re: A certain class consists of 8 students, including Kim. Each day, three [#permalink] New post   24 Aug 2016, 08:51
Sorry for the confusion. I get it know. Since the left-over tasks are to be done only by the remaining people, one person can only do one task. So in this case both mean the same.
avatar
B
a12bansal
Intern
Intern
Joined: 13 Dec 2018
Posts: 20
Own Kudos [?]: 4 [0]
Given Kudos: 34
Send PM
Reviews Badge
Re: A certain class consists of 8 students, including Kim. Each day, three [#permalink] New post   12 Dec 2019, 07:40
Hi Bunuel ,

Please clarify my below doubts. It will help me a lot in other questions too. I am very much confused.

One can also do: P=C11∗C27C38=38P=C11∗C72C83=38, where C11C11 is # of ways to select Kim, C27C72 is # of ways to select any 2 students out of 7 left and C38C83 is total # of ways to select 3 students from 8;

In your above approach, How you have taken C^1_1 ? I always took C^1_8 as we need to select 1 from 8.

Please reply

Thanks a lot
User avatar
L
Kinshook
GMAT Club Legend
GMAT Club Legend
Joined: 03 Jun 2019
Posts: 5342
Own Kudos [?]: 3962 [0]
Given Kudos: 160
Location: India
Schools: HBS '22 CBS '22 Wharton '22
GMAT 1: 690 Q50 V34
WE:Engineering (Transportation)
Send PM
Reviews Badge
Re: A certain class consists of 8 students, including Kim. Each day, three [#permalink] New post   28 Apr 2020, 09:42
metallicafan wrote:
A certain class consists of 8 students, including Kim. Each day, three tasks must be completed and are assigned as follows: one of the 8 students is selected at random to complete Task A, one of the remaining 7 students is selected at random to complete Task B, and one of the remaining six students is selected at random to complete Task C. What is the probability that Kim will be selected to complete one of the three tasks?

(A) 1/3
(B) 3/8
(C) 1/24
(D) 1/336
(E) 1/512

Show Spoiler
In solved in this way:

Probability of completing Task A:

\(\frac{1}{8} * \frac{7}{7} * \frac{6}{6} = \frac{1}{8}\)

Probability of completing Task B:

\(\frac{7}{8} * \frac{1}{7} * \frac{6}{6} = \frac{1}{8}\)

Probability of completing Task C:

\(\frac{7}{8} * \frac{6}{7} * \frac{1}{6} = \frac{1}{8}\)

Therefore: \(\frac{1}{8} + \frac{1}{8} + \frac{1}{8} = [m]\frac{3}{8}\)[/m]

Is there another way to solve it faster?

Source: Jeff Sackman questions - https://www.gmathacks.com



Probability = 7C2 * 3! / 8C3 * 3! = 7*6*3/8*7*6 = 3/8

IMO B
avatar
B
Jaya6
Manager
Manager
Joined: 09 Jan 2021
Posts: 71
Own Kudos [?]: 12 [0]
Given Kudos: 142
Location: India
Schools: ISB '23 (S)
GPA: 3.2
Send PM
Re: A certain class consists of 8 students, including Kim. Each day, three [#permalink] New post   12 May 2021, 07:12
Bowtie wrote:
I agree with B 3/8

first task = 1/8 chance

second task= 7/8*1/7 = 1/8

third task = 7/8*6/7*1/6 = 1/8

chance that she gets picked for one of these is 1/8+1/8+1/8 or 3/8



Hi, can you explain the reason behind 7/8 and 7/8*6/7?
User avatar
bumpbot
Non-Human User
Joined: 09 Sep 2013
Posts: 32627
Own Kudos [?]: 821 [0]
Given Kudos: 0
Send PM
Re: A certain class consists of 8 students, including Kim. Each day, three [#permalink] New post   05 Jan 2024, 23:49
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
GMAT Club Bot
gmatclubot
Re: A certain class consists of 8 students, including Kim. Each day, three [#permalink]
05 Jan 2024, 23:49
Moderators:
Bunuel
Math Expert
92882 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