Question 22·Easy·Probability and Conditional Probability
The frequency table shows the numbers of men who registered for singing lessons, grouped by voice type.
| Voice type | Number of singers |
|---|---|
| Countertenor | 4 |
| Tenor | 6 |
| Baritone | 10 |
| Bass | 5 |
A total of 25 men registered for the lessons. If one of these singers is selected at random, what is the probability that he is a baritone?
For basic probability questions on the SAT that use tables, first identify the specific category the question asks about (here, baritones), then take its count as the numerator and the total count as the denominator. Form the fraction, simplify it if needed, and convert to a decimal to compare with the answer choices. Double-check that you are using the total group in the denominator, not a subset like only non-baritones.
Hints
Focus on the baritone row
Look only at the row in the table for baritone singers. How many baritones are there?
Recall the basic probability formula
Probability of an event is the number of favorable outcomes divided by the total number of possible outcomes.
Use the total given in the problem
The problem tells you that 25 men registered in total. Use this number in the denominator of your probability fraction.
Convert the fraction to a decimal
After you form the fraction (baritones over total singers), simplify it if possible, and then convert that simplified fraction to a decimal to match the answer choices.
Desmos Guide
Use Desmos to compute the probability
In the Desmos calculator, type 10/25 and press Enter. Then look at the decimal value that Desmos shows; this is the probability as a decimal, which you can match to the closest answer choice.
Step-by-step Explanation
Identify the number of favorable outcomes
The question asks for the probability that a randomly selected singer is a baritone.
From the table, the number of baritones is 10. These are the favorable outcomes (the outcomes we care about).
Identify the total number of possible outcomes
The total number of men who registered is already given as 25.
This is the total number of possible outcomes when one singer is chosen at random.
Write and simplify the probability
Probability is
- Here that is .
Now simplify by dividing numerator and denominator by 5:
So , and written as a decimal is .
Therefore, the correct answer is .