Question 14·Medium·Probability and Conditional Probability
Prices of 14 Different Cars
| Type of car | Priced at no more than $25,000 | Priced greater than $25,000 | Total |
|---|---|---|---|
| Nonhybrid | 5 | 3 | 8 |
| Hybrid | 2 | 4 | 6 |
| Total | 7 | 7 | 14 |
The table above shows information about 14 cars listed for sale on an auto dealership’s website. If one of the cars listed for sale is selected at random, what is the probability that the car selected will be a hybrid car priced at no more than $25,000?
For two-way tables on the SAT, first read the question very carefully to see whether it wants a specific cell, a whole row, a whole column, or a combination. For a probability like “hybrid and priced at no more than $25,000,” go straight to the intersection of the Hybrid row and the no more than $25,000 column to get the favorable count, then use the grand total in the bottom-right as the denominator. Write probability as (cell count) / (total), simplify the fraction, and double-check that you didn’t accidentally condition on a row or column total unless the question explicitly says “given that….”
Hints
Locate the correct cell in the table
Which entry in the table represents cars that are hybrid and priced at no more than $25,000? Look at the intersection of that row and column.
Total number of possible cars
When you pick one car at random from the website, how many cars could you possibly choose from in total? Use the grand total in the bottom-right of the table.
Set up the probability fraction
Probability is always . Put the count from the specific cell over the total number of cars, then simplify the fraction.
Desmos Guide
Confirm the fraction and simplification
In Desmos, type 2/14 into an expression line. Look at the simplified fraction that Desmos shows; match that simplified fraction to one of the answer choices.
Step-by-step Explanation
Identify the favorable outcomes
We want a car that is both hybrid and priced at no more than $25,000.
In the table, this is the cell where the Hybrid row and the Priced at no more than $25,000 column intersect. That number is 2 cars.
Find the total number of possible outcomes
The total number of cars listed is given in the bottom-right corner of the table: 14.
This means there are 14 possible outcomes when one car is chosen at random.
Write and simplify the probability
Probability is
- favorable outcomes / total outcomes
So the probability is . Now simplify this fraction by dividing numerator and denominator by 2:
.
Therefore, the correct answer is .