To solve this problem, we need to calculate the probability of two independent events:

1. Getting a tail on the coin toss.
2. Rolling a number greater than 1 on the die.

Step 1: Probability of getting a tail on the coin toss

A coin has two possible outcomes: heads (H) or tails (T). The probability of getting a tail is:

$P(\text{Tail}) = \frac{1}{2}$

Step 2: Probability of rolling a number greater than 1 on the die

A standard die has 6 faces with the numbers 1, 2, 3, 4, 5, and 6. The event of rolling a number greater than 1 means rolling any of the numbers 2, 3, 4, 5, or 6. There are 5 favorable outcomes out of 6 possible outcomes.

$P(\text{Number greater than 1}) = \frac{5}{6}$

Step 3: Combined Probability

Since the coin toss and the die roll are independent events, the combined probability of both events happening is the product of their individual probabilities:

$P(\text{Tail and Number > 1}) = P(\text{Tail}) \times P(\text{Number > 1}) = \frac{1}{2} \times \frac{5}{6} = \frac{5}{12}$

Final Answer:

The probability of getting a tail on the coin toss and a number greater than 1 on the die roll is $\frac{5}{12}$.

Would you like further explanation or additional questions? Here are some related questions for you:

1. What is the probability of getting a head and a number less than or equal to 3?
2. What is the probability of getting either a tail or a number greater than 4?
3. If two coins are tossed and two dice are rolled, what is the probability of getting two tails and numbers greater than 1 on both dice?
4. How do you calculate the probability of independent events with multiple outcomes?
5. What is the probability of not getting a tail on the coin toss and rolling a number less than or equal to 2?

Tip: When dealing with independent events, remember that you can multiply the individual probabilities to find the probability of both events occurring simultaneously.