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

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

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New post 16 Dec 2010, 01:32
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Difficulty:

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Question Stats:

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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

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

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New post 16 Dec 2010, 02:45
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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
Manager
User avatar
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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New post 16 Dec 2010, 04:13
sorry for the typo...the OA was indeed 65/81..

Kudos to u.!!
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Kudos [?]: 104 [0], given: 8

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

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New post 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
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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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