Final answer:
The set G cannot represent 3-digit numbers less than 100 as 3-digit numbers are >= 100. However, if the set includes two-digit numbers, G = {10, 11, 12, ..., 98, 99}. The sample space for drawing a card from a shuffled mix of green and yellow cards is {Green1, Green2, Green3, Green4, Green5, Yellow1, Yellow2, Yellow3}.
Step-by-step explanation:
The question is related to basic set theory and involves writing a set in roster form. If G is the set of 3-digit numbers less than 100, there is actually a mistake in the definition of the set as 3-digit numbers are always greater than or equal to 100. Given the request, we cannot list 3-digit numbers less than 100 because they do not exist. However, if we are to interpret the question as the set of two-digit numbers less than 100, then G would include numbers from 10 through 99.
The correct roster form for G if we consider two-digit numbers would be:
G = {10, 11, 12, ..., 98, 99}
For the second question, listing the sample space for the colored cards scenario:
- G = card drawn is green
- E = card drawn is even-numbered
The sample space when drawing one card from the shuffled mix would be:
S = {Green1, Green2, Green3, Green4, Green5, Yellow1, Yellow2, Yellow3}
The probability of drawing a green card or an even-numbered card can then be calculated based on this sample space.