Bill randomly selects a number from set A, and Sue randomly

Brent@GMATPrepNow wrote: ↑

Mon May 11, 2020 8:31 am

Set A {1, 2, 3, 4, 5}
Set B {1, 2, 3, 4, 5, 6, 7}
Bill randomly selects a number from set A, and Sue randomly selects a number from set B. What is the probability that Sue’s number is greater than Bill’s number?

A) 4/7
B) 7/12
C) 3/5
D) 2/3
E) 5/7

Answer: A
Source: www.gmatprepnow.com

When we solve this probability question using counting techniques, we quickly see it's a lot of work to (accurately) list and count all the possible outcomes in which Sue's number is greater than Bill's number.

Here's a technique that you may be able to apply with other questions requiring listing in accounting.

GIVEN: Set A {1, 2, 3, 4, 5} and Set B {1, 2, 3, 4, 5, 6, 7}
We're selecting one number from the 5 numbers in set A
And we're selecting one number from the 7 numbers in set B
So, the total number of possible outcomes = (5)(7) = 35

To determine the number of outcomes in which Sue's number is greater than Bill's number, we can create a table that looks like this:


Note: each of the 35 boxes represents one possible outcome.

For example, the box with the star (below) represents the outcome in which Bill select the 1 from set A, and Sue selects the 2 from set B



So, if we place a star in every box in which Sue's number is greater than Bill's number, we get:


So the total number of outcomes in which Sue's number is greater than Bill's number = 1 + 2 + 3 + 4 + 5 + 5 = 20

So, P(Sue's number is greater than Bill's number) = 20/35 = 4/7

Answer: A

Cheers,
Brent