Final answer:
To determine the probability, all possible outcomes of the two dice are considered, and all pairs where the 6-sided die has a smaller number than the 4-sided die are counted. There are 6 such favorable outcomes out of a total of 24 possible outcomes, resulting in a probability of 1/4 or 25%.
Step-by-step explanation:
The question asks for the probability that the number rolled on a 6-sided die is smaller than the number rolled on a 4-sided die. The 6-sided die has faces labeled {1, 2, 3, 4, 5, 6} while the 4-sided die has faces labeled {1, 2, 3, 4}. To find the probability, we consider all possible outcomes of rolling the two dice together, which forms a sample space. The 6-sided die and the 4-sided die are independent events, so the total number of outcomes is the product of the number of outcomes for each die, which is 6*4 = 24 outcomes.
Step-by-step explanation:
- Determine the sample spaces: S₆ = {1, 2, 3, 4, 5, 6} for the six-sided die and S₄ = {1, 2, 3, 4} for the four-sided die.
- Count all possible pairs (x,y) where x is from S₆ and y is from S₄.
- Identify all pairs where x < y.
- Count the number of pairs where x < y.
- Divide the count of favorable pairs by the total number of pairs (24) to calculate the probability.
The favorable pairs, where the number on the 6-sided die is smaller than that on the 4-sided die, are: (1,2), (1,3), (1,4), (2,3), (2,4), and (3,4). That gives us 6 favorable outcomes out of 24 possible outcomes, which gives us a probability of 6/24 = 1/4 or 0.25.