What is the probability of rolling a number less than 5 and then rolling a 4?

To determine the probability of rolling a number less than 5 and then rolling a 4, we need to follow these steps:

1. Identify the probability of rolling a number less than 5 on a six-sided die:

   • The numbers less than 5 on a six-sided die are 1, 2, 3, and 4.
   • There are 4 favorable outcomes (1, 2, 3, 4) out of 6 possible outcomes.
   • Therefore, the probability of rolling a number less than 5 is $\frac{4}{6}$ or $\frac{2}{3}$.

2. Identify the probability of rolling a 4 on a six-sided die:

   • There is only 1 favorable outcome (rolling a 4) out of 6 possible outcomes.
   • Therefore, the probability of rolling a 4 is $\frac{1}{6}$.

3. Calculate the combined probability of both events occurring in sequence:

   • The events are independent, so we multiply the probabilities of each event.
   • The combined probability is $\frac{2}{3} \times \frac{1}{6}$.

4. Perform the multiplication:

   • $\frac{2}{3} \times \frac{1}{6} = \frac{2 \times 1}{3 \times 6} = \frac{2}{18} = \frac{1}{9}$.

Therefore, the probability of rolling a number less than 5 and then rolling a 4 is $\frac{1}{9}$.