To find the probability of selecting a yellow marble, we use the formula for probability:
\[ \text{Probability} = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} \]
In this case, the number of favorable outcomes for selecting a yellow marble is 6 (the number of yellow marbles), and the total number of marbles is 30.
So, the probability of selecting a yellow marble is:
\[ \text{Probability of yellow} = \frac{6}{30} = \frac{1}{5} = 0.2 \]
Now, to estimate the total number of red marbles in the bag if there are 300 marbles, we can set up a proportion based on Evan's sample:
The proportion of red marbles in the sample can be calculated as follows:
\[ \text{Fraction of red marbles} = \frac{9 \text{ (red marbles)}}{30 \text{ (total marbles)}} = \frac{9}{30} = 0.3 \]
Now, we can use this fraction to estimate the total number of red marbles in a bag of 300 marbles:
\[ \text{Estimated number of red marbles} = \text{Fraction of red marbles} \times \text{Total number of marbles in bag} \] \[ \text{Estimated number of red marbles} = 0.3 \times 300 = 90 \]
Putting it all together, the completed sentences are:
The probability of selecting a yellow marble is 0.2.
If there are 300 marbles in the bag, a good estimate for the total number of red marbles in the bag is 90.