Final answer:
The probability of getting an even number on one throw of the loaded die is calculated by diving the sum of the weights of the even faces by the total weight of all faces (12/21), which is approximately 0.5714 or 57.14%.
Step-by-step explanation:
The question involves calculating the probability of getting an even number when rolling a loaded die where the probability for each face is proportional to the number of dots on that face. In a regular fair die scenario, each face has an equal chance of facing up. However, this die is loaded, meaning not all outcomes are equally likely.
First, we need to determine the total weight of the die which is the sum of the dots on all faces: 1+2+3+4+5+6 = 21. Next, we find the weight contribution from the even-numbered faces which are 2, 4, and 6. The sum of these weights is 2+4+6 = 12. To find the probability of rolling an even number, we divide the weight for the even numbers by the total weight. So, the probability is 12/21 or about 0.5714.
Therefore, the probability of getting an even number with one throw of this loaded die is approximately 57.14%.