Short Answer 
The probability of all three coins landing heads is 1/8, while the probability of the sum of two dice being 10 is 1/12. By combining these independent probabilities, the total probability of either event occurring is 5/24.
Step 1: Calculate Probability of Coins Landing Heads
To find the probability of all three coins landing heads, we use the formula for independent events. Each coin has a probability of 1/2 of landing heads. Therefore, for three coins, the calculation is:
- (1/2) x (1/2) x (1/2) = 1/8
Step 2: Calculate Probability of Dice Summing to 10
Next, we need to determine the probability of the sum of two dice being 10. We first identify the favorable outcomes. The pairs that sum to 10 are:
- (4,6)
- (5,5)
- (6,4)
There are 3 favorable outcomes and a total of 36 possible outcomes when rolling two dice:
- Probability = 3/36 = 1/12
Step 3: Combine the Probabilities
Finally, we find the total probability of either all coins landing heads or the dice summing to 10. Since these events are independent, we simply add their individual probabilities:
- 1/8 + 1/12 = 5/24
The combined probability of either event occurring is 5/24.