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Senior Manager  Status: Math is psycho-logical
Joined: 07 Apr 2014
Posts: 402
Location: Netherlands
GMAT Date: 02-11-2015
WE: Psychology and Counseling (Other)
As part of her MBA program, Karen applied for three different  [#permalink]

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Difficulty:   25% (medium)

Question Stats: 76% (01:57) correct 24% (02:21) wrong based on 212 sessions

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As part of her MBA program, Karen applied for three different Spring Break outreach projects, each of which selects its students by a random lottery of its applicants.. If the probability of her being accepted to each individual project is 20%, what is the probability that Karen will be accepted to at least one project?

A. 12/125

B. 4/15

C. 61/125

D. 8/15

E. 113/125
Math Expert V
Joined: 02 Sep 2009
Posts: 58402
Re: As part of her MBA program, Karen applied for three different  [#permalink]

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pacifist85 wrote:
As part of her MBA program, Karen applied for three different Spring Break outreach projects, each of which selects its students by a random lottery of its applicants.. If the probability of her being accepted to each individual project is 20%, what is the probability that Karen will be accepted to at least one project?

A. 12/125

B. 4/15

C. 61/125

D. 8/15

E. 113/125

P(at least one) = 1 - P(none) = 1 - (8/10)^3 = 1 - (4/5)^3 = 61/125.

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Senior Manager  Status: Math is psycho-logical
Joined: 07 Apr 2014
Posts: 402
Location: Netherlands
GMAT Date: 02-11-2015
WE: Psychology and Counseling (Other)
As part of her MBA program, Karen applied for three different  [#permalink]

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1
I found this question in a Veritas prep test I did. I found it interesting because it uses percentages.

So, this is what I did. Being accepted to each individual project has a probability of 20%. Since we are looking for the probability of being accepted to at least one, they way I would procede would be by finding the opposite probability (being accepted to none) and subtracting it from 1.

So, if she has 20/100 chances of being accepted for each, she has 80/100 chances of not being accepted for each.

$$\frac{80}{100}$$ $$=$$$$\frac{8}{10}$$ $$=$$$$\frac{4}{5}$$

$$\frac{4}{5}$$*$$\frac{4}{5}$$*$$\frac{4}{5}$$ = $$\frac{64}{125}$$, and

$$1-$$$$\frac{64}{125}$$ $$=$$$$\frac{61}{125}$$. So, ANS C
Math Expert V
Joined: 02 Aug 2009
Posts: 7971
Re: As part of her MBA program, Karen applied for three different  [#permalink]

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pacifist85 wrote:
I found this question in a Veritas prep test I did. I found it interesting because it uses percentages.

So, this is what I did. Being accepted to each individual project has a probability of 20%. Since we are looking for the probability of being accepted to at least one, they way I would procede would be by finding the opposite probability (being accepted to none) and subtracting it from 1.

So, if she has 20/100 chances of being accepted for each, she has 80/100 chances of not being accepted for each.

$$\frac{80}{100}$$ $$=$$$$\frac{8}{10}$$ $$=$$$$\frac{4}{5}$$

$$\frac{4}{5}$$*$$\frac{4}{5}$$*$$\frac{4}{5}$$ = $$\frac{64}{125}$$, and

$$1-$$$$\frac{64}{125}$$ $$=$$$$\frac{61}{125}$$. So, ANS C

hi pacifist,
good.. this is the best way to do..
it is the smartest and least likely way to be wrong.. _________________
Intern  Joined: 22 Jul 2015
Posts: 2
Re: As part of her MBA program, Karen applied for three different  [#permalink]

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Bunuel,

I get this method: P(at least one) = 1 - P(none) = 1 - (8/10)^3 = 1 - (4/5)^3 = 61/125.
Could you show the longer method. Thank you
EMPOWERgmat Instructor V
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 15268
Location: United States (CA)
GMAT 1: 800 Q51 V49 GRE 1: Q170 V170 Re: As part of her MBA program, Karen applied for three different  [#permalink]

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Hi tytus,

GMAT questions can typically be approached in a number of different ways (some of which are shorter/easier than others). In this prompt, it's easiest/fastest to calculate what we DON'T want to have happen and subtract that from 1. If you wanted to approach this the other way (calculate ALL of the different ways to get accepted to AT LEAST ONE Program, here's how you would do it)...

Probability of exactly 1 program (of the 3):

First Program "yes"; second and third "no"
(1/5)(4/5)(4/5) = 16/125

Second Program "yes"; first and third "no"
(4/5)(1/5)(4/5) = 16/125

Third Program "yes"; first and second "no"
(4/5)(4/5)(1/5) = 16/125

Probability of exactly 2 programs (of the 3):

First and second Program "yes"; third "no"
(1/5)(1/5)(4/5) = 4/125

First and third Program "yes"; second "no"
(1/5)(4/5)(1/5) = 4/125

Second and third Program "yes"; first "no"
(4/5)(1/5)(1/5) = 4/125

Probability of all 3 programs:
(1/5)(1/5)(1/5) = 1/125

Total of all options: 16/125+16/125+16/125+4/125+4/125+4/125+1/125 = 61/25

As you can see, this is somewhat tedious, so learning the most efficient ways to deal with prompts can save you LOTS of time.

GMAT assassins aren't born, they're made,
Rich
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Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 8009
GMAT 1: 760 Q51 V42 GPA: 3.82
Re: As part of her MBA program, Karen applied for three different  [#permalink]

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Forget conventional ways of solving math questions. In PS, IVY approach is the easiest and quickest way to find the answer.

As part of her MBA program, Karen applied for three different Spring Break outreach projects, each of which selects its students by a random lottery of its applicants.. If the probability of her being accepted to each individual project is 20%, what is the probability that Karen will be accepted to at least one project?

A. 12/125

B. 4/15

C. 61/125

D. 8/15

E. 113/125

Since the probability of Karen's being accepted to each individual project is 20%, the probability of her not being accepted to each project is 80%. The probability that she will be accepted to none is, therefore, (4/5)*(4/5)*(4/5)=64/125.

Since the complementary event that Karen will be accepted to at least one project is that she will be accepted to none, the probability that Karen will be accepted to at least one project is 1-(64/125)= 61/125.

The answer is (C)
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Re: As part of her MBA program, Karen applied for three different  [#permalink]

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EMPOWERgmatRichC - very helpful, thank you.
Target Test Prep Representative G
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Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2816
Re: As part of her MBA program, Karen applied for three different  [#permalink]

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pacifist85 wrote:
As part of her MBA program, Karen applied for three different Spring Break outreach projects, each of which selects its students by a random lottery of its applicants.. If the probability of her being accepted to each individual project is 20%, what is the probability that Karen will be accepted to at least one project?

A. 12/125

B. 4/15

C. 61/125

D. 8/15

E. 113/125

We can use the equation:

P(accepted to at least one project) = 1 - P(accepted to no projects)

P(accepted to no projects) = 4/5 x 4/5 x 4/5 = 64/125

P(accepted to at least one project) = 1 - 64/125 = 61/125

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Director  G
Joined: 20 Feb 2015
Posts: 764
Concentration: Strategy, General Management
As part of her MBA program, Karen applied for three different  [#permalink]

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pacifist85 wrote:
As part of her MBA program, Karen applied for three different Spring Break outreach projects, each of which selects its students by a random lottery of its applicants.. If the probability of her being accepted to each individual project is 20%, what is the probability that Karen will be accepted to at least one project?

A. 12/125

B. 4/15

C. 61/125

D. 8/15

E. 113/125

1-64/125 is the best way to do it.
Though just in case , if some body wants to kill 4 minutes as I did .

probability of her selection=20%=1/5
not her selection = 4/5

we have 3 places , and she can fill 1,2 or 3 seats.
no of ways she can fill 1 out of 3 = 3c1
no of ways she can fill 2 out of 3=3c2
and for all 3= 3c3
p(one seat)=3*(1/5*4/5*4/5)=3*16/5=48/5
p(two seats)=3*(1/5*1/5*4/5)=3*4/125=12/125
p(all 3 seats)=1*1/125=1/125

summing all 3
we have 61/125
Non-Human User Joined: 09 Sep 2013
Posts: 13244
Re: As part of her MBA program, Karen applied for three different  [#permalink]

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_________________ Re: As part of her MBA program, Karen applied for three different   [#permalink] 03 Oct 2019, 10:08
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