Find all School-related info fast with the new School-Specific MBA Forum

 It is currently 26 Oct 2016, 23:38

### 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

# Probabilty Problem

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

### Show Tags

08 Feb 2011, 13:55
00:00

Difficulty:

(N/A)

Question Stats:

100% (01:01) correct 0% (00:00) wrong based on 2 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.

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

_________________

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: 35311
Followers: 6646

Kudos [?]: 85799 [0], given: 10252

### 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: 2021
Followers: 159

Kudos [?]: 1626 [0], given: 376

### 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%
_________________
Re: Probabilty Problem   [#permalink] 08 Feb 2011, 14:11
Similar topics Replies Last post
Similar
Topics:
Probabilty Letters 4 14 Dec 2011, 01:52
A math problem,s 2 07 Aug 2011, 05:02
probabilty problem "Sam & Jessica" 5 26 Jul 2010, 23:27
probabilty, urgent help ! 2 19 Jul 2010, 03:07
Percentage problem 5 28 Apr 2009, 19:26
Display posts from previous: Sort by