When determining the probability of sequential independent events, you need to consider the probability of each event happening separately and then multiply these probabilities.
1. Determine the probability of rolling a 3 on the first roll:
- A standard die has 6 sides, and each side (including 3) has an equal probability of landing face up.
- Therefore, the probability of rolling a 3 on a standard 6-sided die is [tex]\(\frac{1}{6}\)[/tex].
2. Determine the probability of rolling a 6 on the second roll:
- Similarly, the probability of rolling a 6 on a standard die remains [tex]\(\frac{1}{6}\)[/tex], since each roll of the die is an independent event.
3. Calculate the combined probability of both events occurring in sequence:
- Since the two events are independent, the combined probability of both events happening (rolling a 3 first and then a 6) is the product of their individual probabilities.
The calculation is as follows:
[tex]\[ \text{Probability of rolling a 3 on the first roll} = \frac{1}{6} \approx 0.16666666666666666 \][/tex]
[tex]\[ \text{Probability of rolling a 6 on the second roll} = \frac{1}{6} \approx 0.16666666666666666 \][/tex]
[tex]\[ \text{Combined probability} = \left(\frac{1}{6}\right) \times \left(\frac{1}{6}\right) = \frac{1}{36} \approx 0.027777777777777776 \][/tex]
Thus, the probability of rolling a 3 on the first roll and a 6 on the second roll is approximately [tex]\(0.027777777777777776\)[/tex].
