To find the probability that Nicole will pull out a red marble, we first need to figure out how many red marbles are in the bowl.
- Total Marbles: There are 120 marbles in the bowl.
- Black and White Marbles: We know there are 80 black marbles and 28 white marbles.
To find the number of red marbles, we can subtract the number of black and white marbles from the total number of marbles:
- Number of black marbles: 80
- Number of white marbles: 28
Now, we add the black and white marbles together:
\[ 80 + 28 = 108 \]
Now, we subtract this total from the total number of marbles to find the number of red marbles:
\[ 120 - 108 = 12 \]
So, there are 12 red marbles in the bowl.
- Finding the Probability: Probability is calculated by taking the number of successful outcomes (in this case, pulling a red marble) and dividing it by the total number of outcomes (total marbles).
The probability \( P \) of pulling a red marble is:
\[ P(\text{red marble}) = \frac{\text{Number of red marbles}}{\text{Total number of marbles}} \]
Plugging in the numbers you found:
\[ P(\text{red marble}) = \frac{12}{120} \]
- Simplifying the Probability: We can simplify \( \frac{12}{120} \) by dividing both the numerator and the denominator by 12:
\[ \frac{12 \div 12}{120 \div 12} = \frac{1}{10} \]
So, the probability that Nicole will pull out a red marble is \( \frac{1}{10} \).
- Final Answer: In words, the probability that Nicole will pull a red marble out of the bowl is 1 chance out of 10, or 10%.
That makes sense because there are 12 red marbles out of 120 marbles total, which is a small group compared to the others.