random sum equals 9

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EricKryk: Senior | Next Rank: 100 Posts; Posts: 83; Joined: Tue Mar 31, 2009 11:03 am; Thanked: 3 times

by EricKryk » Fri Jan 24, 2014 9:30 am

A = {2, 3, 4, 5}
B = {4, 5, 6, 7, 8}

Two integers will be randomly selected from the sets above, one integer from set A and one integer from set B. What is the probability that the sum of the two integers equal 9?

A) 0.15
B) 0.20
C) 0.25
D) 0.30
E) 0.33

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Source: Beat The GMAT — Problem Solving | Fri Jan 24, 2014 9:30 am

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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 » Fri Jan 24, 2014 9:37 am

EricKryk wrote:A = {2, 3, 4, 5}
B = {4, 5, 6, 7, 8}

Two integers will be randomly selected from the sets above, one integer from set A and one integer from set B. What is the probability that the sum of the two integers equal 9?

A) 0.15
B) 0.20
C) 0.25
D) 0.30
E) 0.33

Here's a quick solution.
First randomly select a number from set A.
At this point, you can see that, of the 5 numbers in set B, only 1 of them will combine with your number from set A to create a sum of 9.

So, the probability of getting a sum of must = [spoiler]1/5 = 0.2 = B[/spoiler]

Cheers,
Brent

Last edited by Brent@GMATPrepNow on Mon May 18, 2015 6:04 am, edited 2 times in total.

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Patrick_GMATFix: GMAT Instructor; Posts: 1052; Joined: Fri May 21, 2010 1:30 amFollowed by: 98 members; Thanked: 335 times

by Patrick_GMATFix » Fri Jan 24, 2014 9:43 am

Find out the number of pairs that add up to 9 and put that over all possible pairs to find the requested probability. The solution below is taken from the GMATFix App.

-Patrick

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[email protected]: Elite Legendary Member; Posts: 10392; Joined: Sun Jun 23, 2013 6:38 pmFollowed by: 511 members; Location: Palo Alto, CA; Thanked: 2867 times; GMAT Score:800

by [email protected] » Fri Jan 24, 2014 6:55 pm

Hi EricKryk,

Probability questions are based on the probability formula:

(Number of ways that you "want") / (Total number of ways possible)

Since it's usually easier to calculate the total number of possibilities, I'll do that first. There are 4 options for set A and 5 options for set B; since we're choosing one option from each, the total possibilities = 4 x 5 = 20

Now, to figure out the number of duos that sum to 9:

2 and 7
3 and 6
4 and 5
5 and 4

4 options that give us what we "want"

4/20 = 1/5 = 20% = .2 = B

GMAT assassins aren't born, they're made,
Rich

Contact Rich at [email protected]

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sanju09: GMAT Instructor; Posts: 3650; Joined: Wed Jan 21, 2009 4:27 amFollowed by: 80 members; Location: India; Thanked: 267 times; GMAT Score:760

by sanju09 » Fri Jan 24, 2014 10:39 pm

EricKryk wrote:A = {2, 3, 4, 5}
B = {4, 5, 6, 7, 8}

Two integers will be randomly selected from the sets above, one integer from set A and one integer from set B. What is the probability that the sum of the two integers equal 9?

A) 0.15
B) 0.20
C) 0.25
D) 0.30
E) 0.33

For any integer selected from the 4 in set A, we've 5 ways to club it with an integer from set B. Hence, the total number of ways to select two integers this way are (4)(5) = 20. The favorable ways are 2 + 7, 3 + 6, 4 + 5, and 5 + 4, 4 in number.

Required probability = [spoiler]4/20 or 0.20.

Pick B[/spoiler]

The mind is everything. What you think you become. -Lord Buddha

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Quantitative Instructor
The Princeton Review - Manya Abroad
Lucknow-226001

www.manyagroup.com

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Jeff@TargetTestPrep: GMAT Instructor; Posts: 1462; Joined: Thu Apr 09, 2015 9:34 amFollowed by: 22 members; Location: New York, NY; Thanked: 39 times

by Jeff@TargetTestPrep » Mon May 18, 2015 5:55 am

EricKryk wrote:A = {2, 3, 4, 5}
B = {4, 5, 6, 7, 8}

Two integers will be randomly selected from the sets above, one integer from set A and one integer from set B. What is the probability that the sum of the two integers equal 9?

A) 0.15
B) 0.20
C) 0.25
D) 0.30
E) 0.33

Solution:

To determine the probability that the sum of the two integers will equal 9, we must first recognize that probability = (favorable outcomes)/(total outcomes).

Let's first determine the total number of outcomes. We have 4 numbers in set A, and 5 in set B, and since we are selecting 1 number from each set, the total number of outcomes is 4 x 5 = 20.

For our favorable outcomes, we need to determine the number of ways we can get a number from set A and a number from set B to sum to 9. We are selecting from the following two sets:

A = {2, 3, 4, 5}

B = {4, 5, 6, 7, 8}

We will denote the first number as from set A and the second from set B. Here are the pairings that yield a sum of 9:

2,7
3,6
4,5
5,4

We see that there are 4 favorable outcomes. Thus, our probability is 4/20 = 0.25, Answer C.

Jeffrey Miller
Head of GMAT Instruction
[email protected]

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