SAT Practice Exam

« Previous Problem - Statistics: Mean, Median, Mode    Next Problem - Triangle Inequality »

Probability Basics

A special lottery is to be held to select a high school student of the year. There are 800 seniors, 500 juniors, and 100 sophomores who applied. Each senior's name is placed in the lottery 3 times; each junior's name, 4 times; and each sophomore's name, 4 times. What is the probability that a senior's name will be chosen?

---

Answer
This is a probability problem where we need to first determine total ballots per grade level.

Determine Number of Senior ballots

Senior Ballots = # of Seniors x Ballots Cast
Senior Ballots = 800 x 3
Senior Ballots = 2400

Determine Number of Junior ballots

Junior Ballots = # of Juniors x Ballots Cast
Junior Ballots = 500 x 4
Junior Ballots = 2000

Determine Number of Sophomore ballots

Sophomore Ballots = # of Sophomores x Ballots Cast
Sophomore Ballots = 100 x 4
Sophomore Ballots = 400

Now that we have the ballots by grade level, we add all of those up to determine total ballots cast

Determine Number of Total ballots

Total Ballots = Senior Ballots + Junior Ballots + Sophomore Ballots
Total Ballots = 2400 + 2000 + 400
Total Ballots = 4800

Look closely, the problem asks for the probability of a senior name being chosen

When dealing with basic probability problems, we need to find the ratio of our target group over our total group. In this case, the target group is our seniors, so our probability is denoted below

Probability of a Senior Being Chosen  =	Probability of Senior Ballot
	Probability of Total Ballots

Probability of a Senior Being Chosen  =	2400
	4800

From this lesson, our Greatest Common Factor (GCF) of (2400,4800) = 2400

Because our GCF is not equal to 1, our probability is not simplified. The SAT exam will most likely give you the answer in reduced form, so we need to simplify our probability to get our final answer.

Reduce our probability numerator by our GCF = 2400

Reduced Probability Numerator  =	2400
	2400

Reduced Probability Numerator = 1

Reduce our probability denominator by our GCF = 2400

Reduced Probability Denominator  =	4800
	2400

Reduced Probability Denominator = 2

Determine Final Probability using our GCF

Probability of a Senior Being Chosen  =	1
	2