To find the probability, let's break it down:

1. First Roll: You want to roll a 1 or a 3. Since a six-sided die has 6 faces, the probability of rolling either a 1 or a 3 is: $P(\text{first roll is 1 or 3}) = \frac{2}{6} = \frac{1}{3}$

2. Second Roll: You want to roll a 4 or a 6. Similarly, the probability of rolling either a 4 or a 6 is: $P(\text{second roll is 4 or 6}) = \frac{2}{6} = \frac{1}{3}$

Since these two rolls are independent, we multiply the probabilities for the two events: $P(\text{first roll is 1 or 3 and second roll is 4 or 6}) = P(\text{first roll is 1 or 3}) \times P(\text{second roll is 4 or 6}) = \frac{1}{3} \times \frac{1}{3} = \frac{1}{9}$

$\frac{1}{9} \approx 0.111$

Thus, the probability is 0.111.

Answer:

The correct answer is 0.111.

Would you like a more detailed breakdown or further explanation on any step? Here are some follow-up questions to expand on this topic:

1. How would the probability change if you rolled the die three times instead of two?
2. How can the concept of conditional probability apply in this scenario?
3. If you changed the dice to a ten-sided die, how would the probabilities adjust?
4. What is the probability of rolling a number other than 1, 3, 4, or 6 on both rolls?
5. How would the probability be affected if the dice rolls were dependent events?

Tip: When solving probability problems with multiple independent events, always multiply the probabilities for each event to get the combined probability.