GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

 It is currently 18 Feb 2020, 23:17

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

A shipment of 250 smartphones contains 84 that are defecti

Author Message
TAGS:

Hide Tags

Manager
Joined: 09 Feb 2013
Posts: 111
A shipment of 250 smartphones contains 84 that are defecti  [#permalink]

Show Tags

22 Mar 2013, 00:07
6
9
00:00

Difficulty:

45% (medium)

Question Stats:

67% (02:08) correct 33% (02:08) wrong based on 288 sessions

HideShow timer Statistics

A shipment of 250 smartphones contains 84 that are defective. If a customer buys two smartphones at random from the shipment, what is the approximate probability that both phones are defective?

A. 1/250
B. 1/84
C. 1/11
D. 1/9
E. 1/3
GMAT Tutor
Status: Tutor - BrushMyQuant
Joined: 05 Apr 2011
Posts: 631
Location: India
Concentration: Finance, Marketing
Schools: XLRI (A)
GMAT 1: 700 Q51 V31
GPA: 3
WE: Information Technology (Computer Software)
Re: A shipment of 250 smartphones contains 84 that are defecti  [#permalink]

Show Tags

22 Mar 2013, 00:14
3
1
emmak wrote:
A shipment of 250 smartphones contains 84 that are defective. If a customer buys two smartphones at random from the shipment, what is the approximate probability that both phones are defective?
a)$$\frac{1}{250}$$
b)$$\frac{1}{84}$$
c)$$\frac{1}{11}$$
d)$$\frac{1}{9}$$
e)$$\frac{1}{3}$$

Probability of chosing one defective phone from a lot of 250 which ontains 84 defective phones is = (84/250)
Probability of chosing one defective phone from a lot of 249(we already picked one) which ontains 83(we already picked one) defective phones is = (83/249)

Combined probability of series of events = product of the probabilities = (84/250)*(83/249)

84/250 is close to (1/3) and (83/249)= (1/3)
so answer is (1/3)*(1/3) = (1/9)

Hope it helps!
_________________
Intern
Status: Studying
Joined: 09 Dec 2012
Posts: 26
Location: Russian Federation
Concentration: Finance, Strategy
GMAT Date: 04-06-2013
GPA: 3.6
WE: Consulting (Insurance)
Re: A shipment of 250 smartphones contains 84 that are defecti  [#permalink]

Show Tags

08 Jul 2013, 13:43
Amm... this doesn't seem that difficult.

The only problem is quickly identifying that 84 is one third.

Chances of picking 1 defective phone = 84 / 250 = ~0.33 (25/8 is even faster)
Chances of picking 2 phones then = 0.33 x 0.33 = 1/3 x 1/3 = 1/9
If we need to go further = 1/3 x 1/3 x 1/3 = 1/27

Lotto goes on ))
Intern
Joined: 04 May 2013
Posts: 38
Re: A shipment of 250 smartphones contains 84 that are defecti  [#permalink]

Show Tags

08 Jul 2013, 14:48
same as what the other two said.

Probability that the first phone is defective is (84/250) ~ (80*3 = 240). Therefore the approximation is (1/3)
Assuming that the first is a favorable outcome, for the next phone there will only be (83/249). Again, the approximation is ~ (1/3)

Probability of both events happening = (1/3)*(1/3) = 1/9 = D
Intern
Joined: 15 Aug 2011
Posts: 14
Location: United States
Concentration: Marketing, Technology
GPA: 3.6
WE: Project Management (Computer Software)
Re: A shipment of 250 smartphones contains 84 that are defecti  [#permalink]

Show Tags

08 Jul 2013, 20:23
emmak wrote:
A shipment of 250 smartphones contains 84 that are defective. If a customer buys two smartphones at random from the shipment, what is the approximate probability that both phones are defective?

A. 1/250
B. 1/84
C. 1/11
D. 1/9
E. 1/3

$$84C2/250C2 = (84*83)/(250*249)= 14/125 = 1/9$$

Note: This is same as picking 2 red colored cards in random from a deck of 52 cards.....
Current Student
Joined: 18 Oct 2014
Posts: 784
Location: United States
GMAT 1: 660 Q49 V31
GPA: 3.98
Re: A shipment of 250 smartphones contains 84 that are defecti  [#permalink]

Show Tags

26 May 2016, 08:06
emmak wrote:
A shipment of 250 smartphones contains 84 that are defective. If a customer buys two smartphones at random from the shipment, what is the approximate probability that both phones are defective?

A. 1/250
B. 1/84
C. 1/11
D. 1/9
E. 1/3

probability of selecting two defective phones= 84/250*83/249= 1/9

_________________
I welcome critical analysis of my post!! That will help me reach 700+
Target Test Prep Representative
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2801
Re: A shipment of 250 smartphones contains 84 that are defecti  [#permalink]

Show Tags

15 May 2018, 15:17
emmak wrote:
A shipment of 250 smartphones contains 84 that are defective. If a customer buys two smartphones at random from the shipment, what is the approximate probability that both phones are defective?

A. 1/250
B. 1/84
C. 1/11
D. 1/9
E. 1/3

The probability of getting two defective smartphones is:

84/250 x 83/249 ≈ 1/3 x 1/3 = 1/9

_________________

Jeffrey Miller

Jeff@TargetTestPrep.com
181 Reviews

5-star rated online GMAT quant
self study course

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

If you find one of my posts helpful, please take a moment to click on the "Kudos" button.

Manager
Joined: 24 Sep 2018
Posts: 134
Re: A shipment of 250 smartphones contains 84 that are defecti  [#permalink]

Show Tags

22 Oct 2018, 08:16
Veritas Prep Official Solution:

This is dependent probability, so start by setting up your conditions. The odds that the first phone is defective are 84/250. Assume the customer gets that first defective phone. Now one defective phone has been removed, so the odds that second phone is defective are 83/249, since only 83 defective phones and 249 total phones remain. Now we have 84/250 * 83/249, which looks awful. but remember that the GMAT doesn’t tend to give us random, unworkable numbers: there must be a shortcut. 83/249 simplifies perfectly to 1/3, while 84/250 can be simplified as 42/125. Multiplying these together gives us 42/375. 42 goes into 375 almost exactly nine times, so 42/375 is close to 1/9.
Non-Human User
Joined: 09 Sep 2013
Posts: 14086
Re: A shipment of 250 smartphones contains 84 that are defecti  [#permalink]

Show Tags

01 Dec 2019, 14:57
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.
_________________
Re: A shipment of 250 smartphones contains 84 that are defecti   [#permalink] 01 Dec 2019, 14:57
Display posts from previous: Sort by