Probability Basics
A special lottery is to be held to select a high school student of the year. There are 800 seniors, 100 juniors, and 600 sophomores who applied. Each senior's name is placed in the lottery 4 times; each junior's name, 5 times; and each sophomore's name, 3 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 CastSenior Ballots = 800 x 4
Senior Ballots = 3200
Determine Number of Junior ballots
Junior Ballots = # of Juniors x Ballots CastJunior Ballots = 100 x 5
Junior Ballots = 500
Determine Number of Sophomore ballots
Sophomore Ballots = # of Sophomores x Ballots CastSophomore Ballots = 600 x 3
Sophomore Ballots = 1800
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 BallotsTotal Ballots = 3200 + 500 + 1800
Total Ballots = 5500
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 = | 3200 |
| 5500 |
From this lesson, our Greatest Common Factor (GCF) of (3200,5500) = 3200
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 = 3200
| Reduced Probability Numerator = | 3200 |
| 3200 |
Reduced Probability Numerator = 1
Reduce our probability denominator by our GCF = 3200
| Reduced Probability Denominator = | 5500 |
| 3200 |
Reduced Probability Denominator = 1.71875
Determine Final Probability using our GCF
| Probability of a Senior Being Chosen = | 1 |
| 1.71875 |
