To solve this probability problem, let's break it down step by step:

1. Coin flips:

   • When you flip a fair coin, the probability of getting heads on any single flip is $\frac{1}{2}$.
   • Since the coin is flipped twice, and we want two heads, the probability of this is: $P(\text{two heads}) = \frac{1}{2} \times \frac{1}{2} = \frac{1}{4}.$

2. Die roll:

   • A standard six-sided die has six faces (1 through 6). The probability of rolling a 2 is: $P(\text{rolling a 2}) = \frac{1}{6}.$

3. Combined probability:

   • Since the events are independent (the coin flips don't affect the die roll), we multiply the individual probabilities: $P(\text{two heads and rolling a 2}) = \frac{1}{4} \times \frac{1}{6} = \frac{1}{24}.$

Thus, the probability of getting two heads and rolling a 2 is $\frac{1}{24}$.

Would you like more details or have any questions about this problem?

Here are 5 related questions:

1. What is the probability of getting one head and rolling a 4?
2. If you flip the coin three times, what is the probability of getting three heads?
3. What is the probability of getting two tails and rolling a 1?
4. If the die is rolled twice, what is the probability of getting two heads and rolling two 2's?
5. How does the probability change if you flip a biased coin?

Tip: When events are independent, multiply the probabilities of each event to find the overall probability.