To find the probability that Nicole will pull a red marble out of the bowl, we first need to determine how many red marbles there are in the bowl.
- Total Marbles in the Bowl: 120
- Black Marbles: 80
- White Marbles: 28
Now, we'll figure out how many marbles are red by subtracting the number of black and white marbles from the total number of marbles.
\[ \text{Number of Red Marbles} = \text{Total Marbles} - (\text{Black Marbles} + \text{White Marbles}) \]
Calculating the number of red marbles:
\[ \text{Number of Red Marbles} = 120 - (80 + 28) \] \[ = 120 - 108 \] \[ = 12 \]
Now that we know there are 12 red marbles, we can calculate the probability of pulling a red marble.
The formula for probability is:
\[ \text{Probability (P)} = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} \]
In this case, the "favorable outcomes" represent the red marbles, and the "total outcomes" represent all the marbles in the bowl.
So, we can plug in the numbers:
\[ P(\text{Red Marble}) = \frac{\text{Number of Red Marbles}}{\text{Total Marbles}} = \frac{12}{120} \]
Now, we can simplify \(\frac{12}{120}\):
\[ P(\text{Red Marble}) = \frac{12 \div 12}{120 \div 12} = \frac{1}{10} \]
This means that the probability that Nicole will pull a red marble out of the bowl is \(\frac{1}{10}\).
Final Answer: The probability that Nicole will pull a red marble is \(\frac{1}{10}\) or 10%.