Question 7·Easy·Probability and Conditional Probability
| Color | Number |
|---|---|
| Red | 8 |
| Blue | 10 |
| Green | 22 |
| Total | 40 |
The table shows the number of marbles of each color in a bag. If a marble is chosen at random from the bag, what is the probability that the marble will be blue?
For table-based probability questions, immediately identify two things: (1) the total number of items (from the Total row or by adding all categories) for the denominator, and (2) the count that matches the event described in the question (here, blue marbles) for the numerator. Write probability as a simple fraction (favorable)/(total), then look for that exact fraction—or an equivalent simplified fraction—among the answer choices, being careful not to accidentally use the count of a different category or the count of “not” that category.
Hints
Use the total row
First, find how many marbles there are in all. Look at the Total row of the table. This number will be the denominator of your probability fraction.
Focus on blue marbles
Now find the number of blue marbles in the table. This number will be the numerator of your probability fraction.
Recall the basic probability formula
For a simple situation like this, probability (number of favorable outcomes) (total number of outcomes). Write this as a fraction using the numbers from the table.
Desmos Guide
Enter the probability expression
In a new Desmos expression line, type (number of blue marbles)/(total number of marbles) using the values from the table, then press Enter. Desmos will display the decimal value of this probability.
Compare answer choices as decimals
In separate lines, type each answer choice fraction (for example, 30/40, 22/40, 18/40, etc.) and press Enter after each one. Compare the decimal for each choice to the decimal from your probability expression; the correct answer choice is the one whose decimal matches the probability expression exactly.
Step-by-step Explanation
Identify the total number of marbles
Look at the Total row of the table. It shows there are marbles in the bag altogether. This is the denominator (bottom number) of the probability fraction, because all marbles are possible outcomes.
Identify the number of blue marbles
Find the row labeled Blue. The table shows there are blue marbles. This is the numerator (top number) of the probability fraction, because these are the favorable outcomes (getting a blue marble).
Write the probability as a fraction and match the answer choice
The probability of choosing a blue marble is
So the correct answer choice is .