Check GMAT Club Decision Tracker for the Latest School Decision Releases https://gmatclub.com/AppTrack

 It is currently 28 Apr 2017, 16:44

### 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

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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# A state auto-inspection station has two teams. Team 1 is lenient and

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:

### Hide Tags

Intern
Joined: 01 Nov 2010
Posts: 7
Location: NJ
Schools: Rutgers MQF
WE 1: 2 years IT
Followers: 0

Kudos [?]: 1 [0], given: 0

A state auto-inspection station has two teams. Team 1 is lenient and [#permalink]

### Show Tags

08 Feb 2011, 13:55
1
This post was
BOOKMARKED
00:00

Difficulty:

(N/A)

Question Stats:

100% (01:01) correct 0% (00:00) wrong based on 4 sessions

### HideShow timer Statistics

Hey guys, this is a probability problem that you probably wont find on the GMAT. It is out of my book for my probability class that I'm in right now. Either way, it's a quality problem and pertains to probability/combinatorics and is useful practice.

A state auto-inspection station has two teams. Team 1 is lenient and passes all automobiles of a recent vintage; team 2 rejects all autos on first inspection because their "headlights are not properly adjusted." Four unsuspecting drivers take their autos to the station for inspection on four different days and randomly select one of the two teams.

A) If all four cars are new and in excellent condition, what is the probability that three of the four will be rejected?

B) What is the probability that all four will pass?

[Reveal] Spoiler:
A) 4(1/2)^4 = .25
B) (1/2)^4 = .0625

_________________

WE ARE!
"Believe deep down in your heart that you're destined to do great things." - Joe Paterno
You must learn to walk before you can run.

Math Expert
Joined: 02 Sep 2009
Posts: 38297
Followers: 7577

Kudos [?]: 103237 [0], given: 11369

Re: A state auto-inspection station has two teams. Team 1 is lenient and [#permalink]

### Show Tags

08 Feb 2011, 14:10
PennState08 wrote:
Hey guys, this is a probability problem that you probably wont find on the GMAT. It is out of my book for my probability class that I'm in right now. Either way, it's a quality problem and pertains to probability/combinatorics and is useful practice.

Q: A state auto-inspection station has two teams. Team 1 is lenient and passes all automobiles of a recent vintage; team 2 rejects all autos on first inspection because their "headlights are not properly adjusted." Four unsuspecting drivers take their autos to the station for inspection on four different days and randomly select one of the two teams.
A) If all four cars are new and in excellent condition, what is the probability that three of the four will be rejected?
B) What is the probability that all four will pass?

[Reveal] Spoiler:
A) 4(1/2)^4 = .25
B) (1/2)^4 = .0625

A. We need the probability of the event that three of the four cars will be rejected (R) and the one will pass (P): $$P(RRRP)=C^3_4*(\frac{1}{2})^3*\frac{1}{2}=\frac{1}{4}$$ - $$C^3_4$$ choosing which three of the four cars will be rejected, $$(\frac{1}{2})^3$$ - the probability of these three being rejected and $$\frac{1}{2}$$ - the probility of the fourth one besing passed;

B. The same way the probability that all four will pass will be: $$P(SSSS)=(\frac{1}{2})^4$$.
_________________
Math Forum Moderator
Joined: 20 Dec 2010
Posts: 2016
Followers: 162

Kudos [?]: 1797 [0], given: 376

Re: A state auto-inspection station has two teams. Team 1 is lenient and [#permalink]

### Show Tags

08 Feb 2011, 14:11
Probability of rejection and passing is equally likely and is 1/2.

P(Rejection) = 1/2
P(Passing) = 1/2

Let's denote Rejection as R
and Passing as P

1. Three rejections out of the four days can happen in following four ways:

PRRR - Car on the second, third and fourth day are rejected
RPRR
RRPR
RRRP

So;
P(3 Rejections) = 4(1/2*1/2*1/2*1/2) = 4/16 = 1/4 = 25%

2. All pass
Can happen in only one way
PPPP

P(4 Passing) = 1/2*1/2*1/2*1/2 = 1/16 = 6.25%
_________________
Intern
Joined: 27 Oct 2016
Posts: 1
Followers: 0

Kudos [?]: 0 [0], given: 0

Re: A state auto-inspection station has two teams. Team 1 is lenient and [#permalink]

### Show Tags

27 Oct 2016, 22:25
Hi,

The second part was easy. The first part I did as following:

We have 4 cars who have to choose 2 possible inspections, so total: 4C2
To fail, 3 of the following cars had to choose the second inspection. Hence: 3C1
To pass, 1 of them had to choose the 1st inspection. Hence: 1C1

So, probability in the 1st case (a) is given by: ((3C1*1C1)/4C2) = 1/4

Is this the best approach?
Re: A state auto-inspection station has two teams. Team 1 is lenient and   [#permalink] 27 Oct 2016, 22:25
Similar topics Replies Last post
Similar
Topics:
3 Two dogsled teams raced across a 300-mile course in Wyoming. Team A 4 29 Aug 2016, 22:39
52 Two teams are distributing information booklets. Team A dist 26 20 Jan 2017, 16:33
27 256 teams play in a state soccer tournament. A team is elimi 11 18 Sep 2016, 12:37
5 A call center has two teams. Each member of Team A was able 7 28 Apr 2016, 23:01
14 A team has to design a flag. The team has six blue strips of 12 17 Apr 2017, 01:04
Display posts from previous: Sort by

# A state auto-inspection station has two teams. Team 1 is lenient and

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics

 Powered by phpBB © phpBB Group and phpBB SEO Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.