Construct the sample space for a probability experiment where a coin is flipped, and then a 10 -sided die is rolled. $H 1, H 2, H 3, H 4, H 5, H 6, H 7, H 8, H 9, H 10, T 1, T 2, T 3, T 4, T 5, T 6, T 7, T 8, T 9, T 10$ This setup was used for a carnival game, and different amounts paid out for certain outcomes. Find the probability of each outcome: (a)There was a head on the coin and an odd number on the die. (b)There was a head on the coin and a prime number on the die. (c) There was a head on the coin and a number less than 3 on one die (c)The probability that there was a head on the coin and a number less than $3 \mid$ on the die is

Step 1 ：Construct the sample space for a probability experiment where a coin is flipped, and then a 10 -sided die is rolled. The sample space is: $H 1, H 2, H 3, H 4, H 5, H 6, H 7, H 8, H 9, H 10, T 1, T 2, T 3, T 4, T 5, T 6, T 7, T 8, T 9, T 10$

Step 2 ：The sample space for this experiment consists of 20 outcomes, as there are 2 possible outcomes for the coin flip (Heads or Tails) and 10 possible outcomes for the die roll (1 through 10).

Step 3 ：To find the probability of each outcome, we need to count the number of favorable outcomes and divide by the total number of outcomes.

Step 4 ：For a head on the coin and an odd number on the die, the favorable outcomes are H1, H3, H5, H7, and H9. So there are 5 favorable outcomes. The probability is \(\frac{5}{20} = 0.25\)

Step 5 ：For a head on the coin and a prime number on the die, the favorable outcomes are H2, H3, H5, and H7. So there are 4 favorable outcomes. The probability is \(\frac{4}{20} = 0.2\)

Step 6 ：For a head on the coin and a number less than 3 on the die, the favorable outcomes are H1 and H2. So there are 2 favorable outcomes. The probability is \(\frac{2}{20} = 0.1\)

Step 7 ：Final Answer: (a) The probability of getting a head on the coin and an odd number on the die is \(\boxed{0.25}\). (b) The probability of getting a head on the coin and a prime number on the die is \(\boxed{0.2}\). (c) The probability of getting a head on the coin and a number less than 3 on the die is \(\boxed{0.1}\).