Probability

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sumanr84: Legendary Member; Posts: 758; Joined: Sat Aug 29, 2009 9:32 pmFollowed by: 2 members; Location: Bangalore,India; Thanked: 67 times

by sumanr84 » Sat Feb 13, 2010 10:04 am

Q. A lot of fifteen items contains five defective items. Two items are drawn at random. What is the probability that the second item drawn will be defective?

OA : [spoiler]1/3[/spoiler]

Pls help me in understanding the approach.

I am on a break !!

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Source: Beat The GMAT — Problem Solving | Sat Feb 13, 2010 10:04 am

ajith: Legendary Member; Posts: 1275; Joined: Thu Sep 21, 2006 11:13 pmFollowed by: 2 members; Location: Arabian Sea; Thanked: 125 times

by ajith » Sat Feb 13, 2010 12:40 pm

sumanr84 wrote:Q. A lot of fifteen items contains five defective items. Two items are drawn at random. What is the probability that the second item drawn will be defective?

OA : [spoiler]1/3[/spoiler]

Pls help me in understanding the approach.

The easy way to tell it is this - we do not know what happened when the first item was drawn - whether it was defective or not so, it can be defective or non defective with a probability of 1/3 (5/15). Since we do not the outcome of the first the probability of the second item drawn is defective is 1/3 itself.

But Given the first one was defective the probability changes

Always borrow money from a pessimist, he doesn't expect to be paid back.

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vscid: Master | Next Rank: 500 Posts; Posts: 212; Joined: Sat Dec 01, 2007 4:19 pm; Thanked: 5 times

by vscid » Sat Feb 13, 2010 12:43 pm

Well I think since both are drawn together and since we know nothing about the other, the probability of the 2nd one as well as the first one is 5/15.

The GMAT is indeed adaptable. Whenever I answer RC, it proficiently 'adapts' itself to mark my 'right' answer 'wrong'.

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komal: Legendary Member; Posts: 777; Joined: Fri Jan 01, 2010 4:02 amFollowed by: 47 members; Location: Mumbai, India; Thanked: 117 times

by komal » Tue Feb 16, 2010 8:32 am

sumanr84 wrote:Q. A lot of fifteen items contains five defective items. Two items are drawn at random. What is the probability that the second item drawn will be defective?

OA : [spoiler]1/3[/spoiler]

Pls help me in understanding the approach.

First item can either be good, or defective. So our possible sets is:

First item: Good, Second item: Defective
OR
First item: Defective, Second item: Defective

The probability is therefore

P = 10/15 * 5/14 + 5/15 * 4/14 = 1/3

https://www.e-gmat.com/

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