A marble is randomly selected from a bag containing 3 red marbles, 3 blue marbles, and 3 green marbles. What is the probability that the selected marble is green?
Understand the Problem
The question is asking for the probability of selecting a green marble from a bag containing red, blue, and green marbles. To solve this, we need to find the total number of marbles and the number of green marbles to calculate the probability.
Answer
The probability that the selected marble is green is $P(\text{green}) = \frac{1}{3}$.
Answer for screen readers
The probability that the selected marble is green is $P(\text{green}) = \frac{1}{3}$.
Steps to Solve
- Count the total number of marbles
We have 3 red, 3 blue, and 3 green marbles.
Total marbles = $3 \text{ (red)} + 3 \text{ (blue)} + 3 \text{ (green)} = 9$
- Count the number of favorable outcomes
The favorable outcomes for selecting a green marble are simply the number of green marbles.
Number of green marbles = 3
- Calculate the probability
The probability of selecting a green marble is given by the formula:
$$ P(\text{green}) = \frac{\text{Number of green marbles}}{\text{Total number of marbles}} $$
Substituting the values we found:
$$ P(\text{green}) = \frac{3}{9} $$
- Simplify the probability
We can simplify $\frac{3}{9}$:
$$ P(\text{green}) = \frac{1}{3} $$
The probability that the selected marble is green is $P(\text{green}) = \frac{1}{3}$.
More Information
The answer $\frac{1}{3}$ means that out of all the marbles, one-third are green. This situation illustrates a basic example of calculating probability based on equally likely outcomes.
Tips
- Not counting the total marbles correctly: Ensure all marbles are accounted for by adding each color correctly.
- Confusing favorable outcomes with total outcomes: Remember, favorable outcomes are only those that meet the specific condition (in this case, green marbles).
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