random sum equals 9

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

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]

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.