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# A shipment of 250 smartphones contains 84 that are defecti

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

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22 Mar 2013, 01:07
5
7
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Difficulty:

45% (medium)

Question Stats:

69% (02:09) correct 31% (02:09) wrong based on 374 sessions

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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

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Re: A shipment of 250 smartphones contains 84 that are defecti  [#permalink]

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22 Mar 2013, 01:14
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!
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Re: A shipment of 250 smartphones contains 84 that are defecti  [#permalink]

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08 Jul 2013, 14:43
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 ))
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Re: A shipment of 250 smartphones contains 84 that are defecti  [#permalink]

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08 Jul 2013, 15:48
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
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Re: A shipment of 250 smartphones contains 84 that are defecti  [#permalink]

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08 Jul 2013, 21:23
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.....
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Re: A shipment of 250 smartphones contains 84 that are defecti  [#permalink]

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26 May 2016, 09:06
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

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Re: A shipment of 250 smartphones contains 84 that are defecti  [#permalink]

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15 May 2018, 16:17
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

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Re: A shipment of 250 smartphones contains 84 that are defecti  [#permalink]

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22 Oct 2018, 09:16
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.
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Re: A shipment of 250 smartphones contains 84 that are defecti   [#permalink] 22 Oct 2018, 09:16
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