Probability

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hey_thr67: Master | Next Rank: 500 Posts; Posts: 299; Joined: Tue Feb 15, 2011 10:27 amFollowed by: 2 members; Thanked: 9 times

by hey_thr67 » Wed Jun 27, 2012 4:23 am

A box contains 3 yellow balls and 5 black balls. One by one, every ball is selected at random without replacement. What is the probability that the fourth ball selected is black?

A: 1/4
B: 1/2
C: 5/8
D: 2/3
E: 3/4

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Source: Beat The GMAT — Problem Solving | Wed Jun 27, 2012 4:23 am

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Anurag@Gurome: GMAT Instructor; Posts: 3835; Joined: Fri Apr 02, 2010 10:00 pmFollowed by: 523 members; Location: Milpitas, CA; Thanked: 1854 times; GMAT Score:770

by Anurag@Gurome » Wed Jun 27, 2012 4:32 am

hey_thr67 wrote:A box contains 3 yellow balls and 5 black balls. One by one, every ball is selected at random without replacement. What is the probability that the fourth ball selected is black?

As we are selecting the balls without replacement, the probability that the fourth ball selected is black is same as the probability that the first ball selected is black.

This is because, before selecting the fourth ball we have 3 yellow balls and 5 black balls in the box.

Hence, required probability = (number of black balls)/(number of total balls) = 5/8

The correct answer is C.

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Wed Jun 27, 2012 6:24 am

This question reminds me of when I was young, and my friends and I would sometimes "draw straws" to randomly select one person for some unpleasant task (like getting wood for the fire, or something dangerous, like jumping off a roof).

So, someone would hold up n pieces of grass (for n guys), and one of those pieces of grass was very short. The person who selected the shortest piece was the one to do the task.

There was always one guy who wanted to choose his piece last. His reasoning was that his chances of drawing the shortest piece was minimized since every person before him had a chance of drawing the short piece before it got to his turn.

The truth of the matter is that all n guys have a 1/n chance of selecting the shortest piece, regardless of when they select.

The same applies to the original question here.

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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