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

1. Rolling a number less than three on a fair die.
2. Getting tails on a coin flip.

Step 1: Probability of Rolling a Number Less Than Three on a Fair Die

A fair die has 6 sides, numbered 1 through 6. The numbers less than three are 1 and 2, so there are 2 favorable outcomes.

The probability of rolling a number less than three is: $P(\text{Number less than 3}) = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} = \frac{2}{6} = \frac{1}{3}$

Step 2: Probability of Getting Tails on a Coin Flip

A fair coin has 2 sides, so the probability of getting tails is: $P(\text{Tails}) = \frac{1}{2}$

Step 3: Combined Probability

Since these two events are independent, the combined probability is the product of the two individual probabilities: $P(\text{Number less than 3 and Tails}) = P(\text{Number less than 3}) \times P(\text{Tails}) = \frac{1}{3} \times \frac{1}{2} = \frac{1}{6}$

Thus, the correct answer is:

$\boxed{\frac{1}{6}}$

Would you like more details, or do you have any other questions?

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Here are 8 related questions:

1. What is the probability of rolling an even number on a fair die and getting heads on a coin flip?
2. If you roll two fair dice, what is the probability that both will show a number less than three?
3. How do you calculate the probability of dependent events?
4. What is the probability of rolling a prime number on a fair die?
5. What is the probability of flipping two coins and getting at least one tail?
6. If a coin is flipped three times, what is the probability of getting exactly two heads?
7. How does the probability change if the die is biased?
8. What is the probability of getting a sum of 7 when rolling two fair dice?

Tip: When calculating the probability of multiple independent events, remember to multiply the probabilities of each event occurring separately.