First, let's determine the total number of marbles in the bag.
The bag contains:
- 1 blue marble
- 2 green marbles
- 3 yellow marbles
- 3 red marbles
To find the total number of marbles, we sum these amounts:
[tex]\[ 1 + 2 + 3 + 3 = 9 \][/tex]
So, there are 9 marbles in total.
Next, we focus on the red marbles. There are 3 red marbles.
The probability of drawing a red marble is the ratio of the number of red marbles to the total number of marbles. This can be expressed as:
[tex]\[ \text{Probability of drawing a red marble} = \frac{\text{Number of red marbles}}{\text{Total number of marbles}} = \frac{3}{9} \][/tex]
We can simplify this fraction:
[tex]\[ \frac{3}{9} = \frac{1}{3} \][/tex]
Thus, the probability of drawing a red marble out of the bag without looking is:
[tex]\[ \boxed{\frac{1}{3}} \][/tex]
