Question 55·Easy·Probability and Conditional Probability
A jar contains the tokens shown.
| Color | Number of tokens |
|---|---|
| Red | 12 |
| Blue | 9 |
| Green | 4 |
If one token is selected at random from the jar, what is the probability that the token is blue?
For basic probability questions with a small table, first find the total number of items by adding all categories. Then identify the count that matches the specific event the question asks about (here, blue tokens). Write the probability as (favorable count)/(total count), reduce the fraction if needed, and match it to the answer choices. Always double-check that you used the correct category from the table.
Hints
Count all the tokens
Before you can find a probability, you need the total number of possible outcomes. Add the red, blue, and green tokens together.
Recall the basic probability formula
Probability of an event equals the number of favorable outcomes divided by the total number of outcomes. What is the event in this question?
Identify favorable outcomes
For this problem, a favorable outcome is drawing a blue token. How many blue tokens are there in the jar?
Desmos Guide
Compute the probability as a fraction in Desmos
In a new expression line, type 9/(12+9+4) to represent (number of blue tokens)/(total tokens). Look at the value (fraction and/or decimal) that Desmos displays; that value is the probability of selecting a blue token.
Step-by-step Explanation
Find the total number of tokens
Add the numbers of each color together to get the total number of tokens in the jar.
- Red tokens: 12
- Blue tokens: 9
- Green tokens: 4
So the total number of tokens is .
Use the probability formula
The probability of an event is
Here, a "favorable outcome" is selecting a blue token.
- Number of favorable outcomes (blue tokens):
- Total number of outcomes (total tokens):
So the probability of selecting a blue token is
which corresponds to choice B.