Problem Solving

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

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

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.