In a drawer of shirts 8 are blue, 6 are green and 4 are mage

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BTGmoderatorDC: Moderator; Posts: 7187; Joined: Thu Sep 07, 2017 4:43 pmFollowed by: 23 members

by BTGmoderatorDC » Tue Sep 17, 2019 4:51 pm

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In a drawer of shirts 8 are blue, 6 are green and 4 are magenta. If Mason draws 2 shirts at random, what is the probability at least one of the shirts he draws will be blue?

(A) 25/153
(B) 28/153
(C) 5/17
(D) 4/9
(E) 12/17

OA E

Source: Princeton Review

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Source: Beat The GMAT — Problem Solving | Tue Sep 17, 2019 4:51 pm

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Jay@ManhattanReview: GMAT Instructor; Posts: 3008; Joined: Mon Aug 22, 2016 6:19 amFollowed by: 34 members; Location: Grand Central / New York; Thanked: 470 times

by Jay@ManhattanReview » Tue Sep 17, 2019 8:26 pm

BTGmoderatorDC wrote:In a drawer of shirts 8 are blue, 6 are green and 4 are magenta. If Mason draws 2 shirts at random, what is the probability at least one of the shirts he draws will be blue?

(A) 25/153
(B) 28/153
(C) 5/17
(D) 4/9
(E) 12/17

OA E

Source: Princeton Review

Given that there are 8 blue, 6 green and 4 magenta color shirts, we have 18 shirts, out of which 8 are blue and 10 are non-blue.

Probability at least one of the shirts is blue = Probability of drawing (One shirt is blue and the other is non-blue + Both shirts are blue)
= (8C1*10C1)/18C2 + 8C2/18C2 = (8C1*10C1+ 8C2)/18C2 = {8*10 + (8*7)/(1.2)} / {(18.17)/(1.2)} = 12/17

The correct answer: E

Hope this helps!

-Jay
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Scott@TargetTestPrep: GMAT Instructor; Posts: 8144; Joined: Sat Apr 25, 2015 10:56 amFollowed by: 29 members; Location: Los Angeles, CA; Thanked: 43 times

by Scott@TargetTestPrep » Tue Sep 24, 2019 10:23 am

BTGmoderatorDC wrote:In a drawer of shirts 8 are blue, 6 are green and 4 are magenta. If Mason draws 2 shirts at random, what is the probability at least one of the shirts he draws will be blue?

(A) 25/153
(B) 28/153
(C) 5/17
(D) 4/9
(E) 12/17

OA E

Source: Princeton Review

We can use the equation:

P(at least one of the shirts he draws will be blue) = 1 - P(no blue shirts)

P(no blue shirts) = 10/18 x 9/17 = 5/9 x 9/17 = 5/17.

So, P(at least one of the shirts he draws will be blue) = 1 - 5/17 = 12/17.

Answer: E

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