In a box of 12 pens, a total of 3 are defective. If a customer buys 2 pens selected at random from the box, what is the

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

by BTGmoderatorDC » Fri Jul 10, 2020 7:05 pm

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In a box of 12 pens, a total of 3 are defective. If a customer buys 2 pens selected at random from the box, what is the probability that neither pen will be defective?

A. 1/6
B. 2/9
C. 6/11
D. 9/16
E. 3/4

OA C

Source: Official Guide

Source: Beat The GMAT — Problem Solving | Fri Jul 10, 2020 7:05 pm

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16206; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

Re: In a box of 12 pens, a total of 3 are defective. If a customer buys 2 pens selected at random from the box, what is

by Brent@GMATPrepNow » Sat Jul 11, 2020 9:14 am

BTGmoderatorDC wrote: ↑
Fri Jul 10, 2020 7:05 pm
In a box of 12 pens, a total of 3 are defective. If a customer buys 2 pens selected at random from the box, what is the probability that neither pen will be defective?

A. 1/6
B. 2/9
C. 6/11
D. 9/16
E. 3/4

OA C

Source: Official Guide

P(neither pen is defective) = P(1st pen selected is NOT defective AND 2nd pen selected is NOT defective)
= P(1st pen selected is NOT defective) x P(2nd pen selected is NOT defective)
= 9/12 x 8/11
= 6/11
= C

ASIDE: How did I get 9/12 and 8/11?
For the first selection, 9 of the 12 pens are good.
For the second selection, we must assume that the first selection resulted in a GOOD pen. This means there are now 11 pens remaining, and 8 of them are GOOD.

Brent Hanneson - Creator of GMATPrepNow.com

ygcrowanhand: Senior | Next Rank: 100 Posts; Posts: 36; Joined: Mon Nov 24, 2014 1:47 pm; Location: London

Re: In a box of 12 pens, a total of 3 are defective. If a customer buys 2 pens selected at random from the box, what is

by ygcrowanhand » Wed May 18, 2022 10:36 am

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