The probabilities of four events are shown. List them in order from least to greatest. \[ \frac{6}{13} \quad 3 \text { out of } 9 \]

To list the probabilities in order from least to greatest, we first need to convert the second probability into a fraction. The probability "3 out of 9" can be written as a fraction: \[ \frac{3}{9} \] Now we can simplify this fraction: \[ \frac{3}{9} = \frac{1}{3} \] Now we have two fractions to compare: \[ \frac{6}{13} \quad \text{and} \quad \frac{1}{3} \] To compare these fractions, we can find a common denominator. The least common multiple (LCM) of 13 and 3 is 39. We will convert both fractions to have a denominator of 39: \[ \frac{6}{13} = \frac{6 \times 3}{13 \times 3} = \frac{18}{39} \] \[ \frac{1}{3} = \frac{1 \times 13}{3 \times 13} = \frac{13}{39} \] Now we can compare the numerators: \[ \frac{13}{39} \quad \text{and} \quad \frac{18}{39} \] Since 13 is less than 18, we have: \[ \frac{1}{3} < \frac{6}{13} \] Therefore, the probabilities listed from least to greatest are: \[ \frac{1}{3} \quad \text{and} \quad \frac{6}{13} \]