Question 28·Easy·Probability and Conditional Probability
Each rock in a collection of 70 rocks was classified as either igneous, metamorphic, or sedimentary, as shown in the frequency table.
| Classification | Frequency |
|---|---|
| igneous | 10 |
| metamorphic | 33 |
| sedimentary | 27 |
If one of these rocks is selected at random, what is the probability of selecting a rock that is igneous?
For basic probability questions on the SAT, always start by identifying the event of interest (here, choosing an igneous rock) and count how many outcomes satisfy that event. Then, find the total number of possible outcomes by adding all relevant categories. Write the probability as “favorable over total” in fraction form, and match that fraction directly to the answer choices—being careful not to mix up the total with just one category or a partial total.
Hints
Focus on the definition of probability
Think about how probability is usually written as a fraction: What goes in the numerator and what goes in the denominator?
Identify the favorable outcomes
From the table, how many rocks are igneous? That number will be the top of your fraction.
Find the total number of rocks
Add the three frequencies (igneous, metamorphic, and sedimentary) to find how many rocks are in the collection altogether. That will be the bottom of your fraction.
Match your fraction to an answer choice
Once you have your probability as a fraction, compare it directly to the options provided and choose the one that is exactly the same.
Desmos Guide
Find the total number of rocks
In a new expression line, type 10+33+27 to compute the total from the table. Desmos will display 70 as the total number of possible outcomes.
Compute the probability fraction
Now type 10/(10+33+27) to compute the probability of selecting an igneous rock. This equals 10/70 (about 0.142857), which matches choice D.
Step-by-step Explanation
Identify what probability means in this context
Probability is:
Here, a "favorable outcome" means selecting an igneous rock. The "total possible outcomes" is the total number of rocks in the collection.
Find the number of favorable outcomes
From the table, the number of igneous rocks is 10. That means there are 10 favorable outcomes (10 ways to pick an igneous rock).
Find the total number of possible outcomes
Add all the frequencies in the table to get the total number of rocks:
- Igneous: 10
- Metamorphic: 33
- Sedimentary: 27
Total:
So there are 70 rocks in the collection.
Write the probability as a fraction
Use the probability formula with the numbers you found:
- Number of favorable outcomes (igneous) = 10
- Total number of outcomes (all rocks) = 70
So the probability is:
Among the answer choices, this matches choice D, so the correct answer is .