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

Redeem

According to a recent student poll

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
Master | Next Rank: 500 Posts
Posts: 418
Joined: Sun Jul 04, 2010 12:48 pm
Thanked: 6 times
Followed by:3 members

According to a recent student poll

by gmatdriller » Sat Nov 22, 2014 9:05 pm
According to a recent student poll, 5/7 of the 21 members of the finance club are interested in a career in investment banking. If two students are chosen at random, what is the probability that at least one of them is interested in investment banking?
A: 1/14 B:4/49 C: 2/7 D:45/49 E: 13/14

OAE
Top
Source: — Problem Solving |

GMAT/MBA Expert

User avatar
Elite Legendary Member
Posts: 10392
Joined: Sun Jun 23, 2013 6:38 pm
Location: Palo Alto, CA
Thanked: 2867 times
Followed by:511 members
GMAT Score:800

by [email protected] » Sat Nov 22, 2014 11:11 pm
Hi gmatdriller,

When it comes to probability questions, there are 2 things that you can calculate: what you WANT and what you DON'T WANT.

In probability, (the probability of what you WANT) + (the probability of what you DON'T WANT) = 1

In this question, we WANT AT LEAST 1 member chosen to be interested in investment banking; what we DON'T WANT is 0 members chosen to be interested in investment banking. The second option will be easier to calculate. Here's how:

We're told that 5/7 of the 21 members are interested in investment banking:

15 interested in investment banking
6 NOT interested in investment banking

We're asked to select 2 at random. Based on the above probability concepts....

1 - (probability that the 2 DON'T WANT investment banking) = the probability of AT LEAST 1 that does want investment banking

The probability that the 1st DOESN'T WANT investment banking = 6/21
The probability that the 2nd DOESN'T WANT investment banking = 5/20

(6/21)(5/20) = 30/420 = 3/42 = 1/14

1 - 1/14 = 13/14 = the probability that AT LEAST 1 of the 2 chosen is interested in investment banking.

Final Answer: E

GMAT assassins aren't born, they're made,
Rich
Contact Rich at [email protected]
Image
Top
Master | Next Rank: 500 Posts
Posts: 418
Joined: Sun Jul 04, 2010 12:48 pm
Thanked: 6 times
Followed by:3 members

by gmatdriller » Sun Nov 23, 2014 7:52 am
Yeah, I did it this way on the 2nd trial and got the correct Ans too.

However, on the first trial I used the chance of picking 2 INTERESTED in Inv Banking:
I got it wrong.

(i) The 1st attempt gives a student wo is interested in Inv Banking OR
(ii) The 2nd attempt produces a student interested in Inv. Banking

15 students interested:

1st attempt right: 15/21
2nd attempt: 1st attempt wrong * 2nd attempt right
[I usually miss out the part in bold.] => 6/21*15/20

So, we have (i) OR (ii)
15/21 + 6/21*15/20 = 26/28 = 13/14

Rich, I would appreciate some examples that rely on this sort of consideration.

Thanks
Top

GMAT/MBA Expert

User avatar
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 Nov 23, 2014 8:13 am
gmatdriller wrote:According to a recent student poll, 5/7 of the 21 members of the finance club are interested in a career in investment banking. If two students are chosen at random, what is the probability that at least one of them is interested in investment banking?
A) 1/14
B) 4/49
C) 2/7
D) 45/49
E) 13/14
There are several ways to solve this question.

First, 15 members are interested in investment banking (IB) and 6 are NOT interested in IB

We want P(have at least 1 interested in IB)
When it comes to probability questions involving "at least," it's best to try using the complement.
That is, P(Event A happening) = 1 - P(Event A not happening)
So, here we get: P(have at least 1 interested in IB) = 1 - P(not have at least 1 interested in IB)
What does it mean to not have at least 1 interested in IB? It means getting ZERO members interested in IB.
So, we can write: P(have at least 1 interested in IB) = 1 - P(have ZERO interested in IB)

Okay, let's go...
P(have ZERO interested in IB) = P(1st person is NOT interested in IB AND 2nd person is NOT interested in IB)
= P(1st person is NOT interested in IB) x P(2nd person is NOT interested in IB)
= 6/21 x 5/20
= 1/14


So, P(at least 1 interested in IB) = 1 - P(not at least 1 interested in IB)
= 1 - 1/14
= [spoiler]13/14[/spoiler]
= E

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
Image
Top

GMAT/MBA Expert

User avatar
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 Nov 23, 2014 8:26 am
According to a recent student poll, 5/7 of the 21 members of the finance club are interested in a career in investment banking. If two students are chosen at random, what is the probability that at least one of them is interested in investment banking?
A) 1/14
B) 4/49
C) 2/7
D) 45/49
E) 13/14
Here's another (longer) approach:

We know that 15 members are INTERESTED
And 6 members are NOT interested.

We want P(have at least 1 INTERESTED)

There are THREE DIFFERENT CASES that satisfy this condition:
case 1: 1st person is INTERESTED and the 2nd person is NOT interested
The probability that this case occurs = (15/21)(6/20) = 3/14
case 2: 1st person is NOT interested and the 2nd person is INTERESTED
The probability that this case occurs = (6/21)(15/20) = 3/14
case 3: 1st person is INTERESTED and the 2nd person is INTERESTED
The probability that this case occurs = (15/21)(14/20) = 1/2

So, P(have at least 1 INTERESTED) = P(case 1 OR case 2 OR case 3)
= P(case 1) + P(case 2) + P(case 3)
= 3/14 + 3/14 + 1/2
= [spoiler]13/14[/spoiler]
= E

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
Image
Top

GMAT/MBA Expert

User avatar
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 Nov 23, 2014 8:34 am
According to a recent student poll, 5/7 of the 21 members of the finance club are interested in a career in investment banking. If two students are chosen at random, what is the probability that at least one of them is interested in investment banking?
A) 1/14
B) 4/49
C) 2/7
D) 45/49
E) 13/14
We can also use COUNTING TECHNIQUES to answer the question.

P(have at least 1 interested in IB) = 1 - P(have ZERO interested in IB)

P(have ZERO interested in IB)
P(have ZERO interested in IB) = (# of ways to select 2 people that are NOT interested in IB)/(# of ways to select 2 people from 21 members)

# of ways to select 2 people that are NOT interested in IB: 6 members are NOT interested in IB
We can select 2 of these members in 6C2 ways.
6C2 = 15

# of ways to select 2 people from 21 members:
We can select 2 of the 21 members in 21C2 ways.
21C2 = 210

So, P(have ZERO interested in IB) = 15/210 = 1/14

So, P(have at least 1 interested in IB) = 1 - P(have ZERO interested in IB)
= 1 - 1/14
= [spoiler]13/14[/spoiler]
= E

If anyone is interested, we have a free video on calculating combinations (like 6C2 and 21C2) in your head: https://www.gmatprepnow.com/module/gmat-counting?id=789

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
Image
Top
Post new topic Post Reply
• Page 1 of 1