BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

probability

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
Source: — Problem Solving |
User avatar
GMAT Instructor
Posts: 1248
Joined: Thu Mar 29, 2012 2:57 pm
Location: Everywhere
Thanked: 503 times
Followed by:192 members
GMAT Score:780

by Bill@VeritasPrep » Fri Mar 30, 2012 7:27 pm
First off, since the question specifically asks about drawing a red ball, we can ignore the fact that we're given 3 colors (black, white, red) and look at the problem as an either/or situation: the ball is either red or not red.

How can we get a red ball on the third draw? Three ways:

NR-NR-R: 6/8 * 5/7 * 2/6 = 10/56
NR-R-R: 6/8 * 2/7 * 1/6 = 1/28
R-NR-R: 2/8 * 6/7 * 1/6 = 1/28

1/28 + 1/28 + 10/56 = 2/56 + 2/56 + 10/56 = 14/56.

Bill
Join Veritas Prep's 2010 Instructor of the Year, Matt Douglas for GMATT Mondays

Visit the Veritas Prep Blog

Try the FREE Veritas Prep Practice Test
Top
Senior | Next Rank: 100 Posts
Posts: 32
Joined: Thu Mar 08, 2012 12:24 am
GMAT Score:670

by ka_t_rin » Thu Apr 05, 2012 2:47 am
Bill@VeritasPrep wrote:First off, since the question specifically asks about drawing a red ball, we can ignore the fact that we're given 3 colors (black, white, red) and look at the problem as an either/or situation: the ball is either red or not red.

How can we get a red ball on the third draw? Three ways:

NR-NR-R: 6/8 * 5/7 * 2/6 = 10/56
NR-R-R: 6/8 * 2/7 * 1/6 = 1/28
R-NR-R: 2/8 * 6/7 * 1/6 = 1/28

1/28 + 1/28 + 10/56 = 2/56 + 2/56 + 10/56 = 14/56.

Bill

Can you tell me why I got another result?
Desired outcomes:
WWR BBR WBR BWR BRR WRR RBR RWR - 8 OUTCOMES

All outcomes 3P8 = 56 thus probability is 8/56 = 1/7

What is my mistake?
Top
Senior | Next Rank: 100 Posts
Posts: 32
Joined: Thu Mar 08, 2012 12:24 am
GMAT Score:670

by ka_t_rin » Thu Apr 05, 2012 2:55 am
ka_t_rin wrote:
Bill@VeritasPrep wrote:First off, since the question specifically asks about drawing a red ball, we can ignore the fact that we're given 3 colors (black, white, red) and look at the problem as an either/or situation: the ball is either red or not red.

How can we get a red ball on the third draw? Three ways:

NR-NR-R: 6/8 * 5/7 * 2/6 = 10/56
NR-R-R: 6/8 * 2/7 * 1/6 = 1/28
R-NR-R: 2/8 * 6/7 * 1/6 = 1/28

1/28 + 1/28 + 10/56 = 2/56 + 2/56 + 10/56 = 14/56.

Bill

Can you tell me why I got another result?
Desired outcomes:
WWR BBR WBR BWR BRR WRR RBR RWR - 8 OUTCOMES

All outcomes 3P8 = 56 thus probability is 8/56 = 1/7

What is my mistake?
I believe I realized what was wrong.
To count desired outcomes we can use slot method starting from the most restricted: 2 for red, 7 and 6 for two others. = 2x7x6
and combinations for all results = 3C8 = 6x7x8
Thus 2x7x6/6x7x8 = 14/56
Top
Legendary Member
Posts: 1159
Joined: Wed Apr 16, 2008 10:35 pm
Thanked: 56 times

by raunekk » Thu Apr 05, 2012 3:17 am
@Bill

If the question would have mentioned - Red ONLY at the third time (not the first and second time), then the answer would have been :

NR-NR-R: 6/8 * 5/7 * 2/6 = 10/56

right?

Thanks in advance.
Last edited by raunekk on Thu Apr 05, 2012 4:11 am, edited 1 time in total.
Top
User avatar
GMAT Instructor
Posts: 15539
Joined: Tue May 25, 2010 12:04 pm
Location: New York, NY
Thanked: 13060 times
Followed by:1906 members
GMAT Score:790

by GMATGuruNY » Thu Apr 05, 2012 3:58 am
Md.Nazrul Islam wrote:A bag contain 3 white balls ,3 black balls ,and 2 red balls .one by one three balls are drawn without replacement .what is the probability that the third ball is red .
The probability of selecting X on the NTH PICK is equal to the probability of selecting X on the FIRST PICK.

On the FIRST pick, P(R) = 2/8 = 1/4.
Thus, on the THIRD PICK, P(R) = 1/4.
The two probabilities are equal.

If the problem asked for the probability that the FOURTH marble is red, the answer would be the same: 1/4.
If the problem asked for the probability that the FIFTH marble is red, the answer would be the same: 1/4.

For other problems that explore this concept, check here:

https://www.beatthegmat.com/manhattan-pr ... 89481.html

https://www.beatthegmat.com/probablity-ques-t60161.html
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.

As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.

For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
Top
User avatar
GMAT Instructor
Posts: 1248
Joined: Thu Mar 29, 2012 2:57 pm
Location: Everywhere
Thanked: 503 times
Followed by:192 members
GMAT Score:780

by Bill@VeritasPrep » Thu Apr 05, 2012 6:53 am
raunekk wrote:@Bill

If the question would have mentioned - Red ONLY at the third time (not the first and second time), then the answer would have been :

NR-NR-R: 6/8 * 5/7 * 2/6 = 10/56

right?

Thanks in advance.
Yup. We need one of the 6 not-reds on the first draw (out of 8 possibilities, one of the 5 remaining not-reds on the second draw (out of 7 possibilities), and one of the 2 reds on the third draw (out of 6 possibilities)
Join Veritas Prep's 2010 Instructor of the Year, Matt Douglas for GMATT Mondays

Visit the Veritas Prep Blog

Try the FREE Veritas Prep Practice Test
Top
Post new topic Post Reply
• Page 1 of 1