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# A certain businessman wears only three different colors of shirt -- wh

Author Message
Manager
Status: Still Struggling
Joined: 03 Nov 2010
Posts: 135

Kudos [?]: 104 [0], given: 8

Location: India
GMAT Date: 10-15-2011
GPA: 3.71
WE: Information Technology (Computer Software)
A certain businessman wears only three different colors of shirt -- wh [#permalink]

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16 Dec 2010, 01:32
00:00

Difficulty:

(N/A)

Question Stats:

67% (00:51) correct 33% (01:12) wrong based on 9 sessions

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A certain businessman wears only three different colors of shirt -- white, blue, and gray. The probability that he will wear a blue or gray shirt is 2/3. During a four-day work week, what is the probability that the businessman will wear a white shirt at least once?

OA:
[Reveal] Spoiler:
65/81

_________________

Knewton Free Test 10/03 - 710 (49/37)
Princeton Free Test 10/08 - 610 (44/31)
Kaplan Test 1- 10/10 - 630
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Kudos [?]: 104 [0], given: 8

Kaplan GMAT Instructor
Joined: 21 Jun 2010
Posts: 146

Kudos [?]: 225 [1], given: 0

Location: Toronto
Re: A certain businessman wears only three different colors of shirt -- wh [#permalink]

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16 Dec 2010, 02:45
1
KUDOS
krishnasty wrote:
A certain businessman wears only three different colors of shirt -- white, blue, and gray. The probability that he will wear a blue or gray shirt is 2/3. During a four-day work week, what is the probability that the businessman will wear a white shirt at least once?

OA: 65/18

Hi!

There's a typo with the OA - you've got the digits in the denominator reversed.

So, let's ignore the "OA" and solve.

For complex probability questions, it's almost always quicker to solve with the "one minus" approach:

Probability (what you want) = 1 - Probability (what you don't want)

Here we want white on at least one day. So, we don't want no white shirts at all.

Since the probability of blue or grey is 2/3,

the probability of no white on any of the 4 days = (2/3)(2/3)(2/3)(2/3) = 16/81

1 - 16/81 = 65/81... done!

Kudos [?]: 225 [1], given: 0

Manager
Status: Still Struggling
Joined: 03 Nov 2010
Posts: 135

Kudos [?]: 104 [0], given: 8

Location: India
GMAT Date: 10-15-2011
GPA: 3.71
WE: Information Technology (Computer Software)
Re: A certain businessman wears only three different colors of shirt -- wh [#permalink]

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16 Dec 2010, 04:13
sorry for the typo...the OA was indeed 65/81..

Kudos to u.!!
_________________

Knewton Free Test 10/03 - 710 (49/37)
Princeton Free Test 10/08 - 610 (44/31)
Kaplan Test 1- 10/10 - 630
Veritas Prep- 10/11 - 630 (42/37)
MGMAT 1 - 10/12 - 680 (45/34)

Kudos [?]: 104 [0], given: 8

Senior Manager
Status: Bring the Rain
Joined: 17 Aug 2010
Posts: 390

Kudos [?]: 47 [0], given: 46

Location: United States (MD)
Concentration: Strategy, Marketing
Schools: Michigan (Ross) - Class of 2014
GMAT 1: 730 Q49 V39
GPA: 3.13
WE: Corporate Finance (Aerospace and Defense)
Re: A certain businessman wears only three different colors of shirt -- wh [#permalink]

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16 Dec 2010, 07:25
This is what I did

1-(Prob of 4 days non white)=1-(2/3)(2/3)(2/3)(2/3)=1-(16/81)=65/81
_________________

Kudos [?]: 47 [0], given: 46

Re: A certain businessman wears only three different colors of shirt -- wh   [#permalink] 16 Dec 2010, 07:25
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