To determine the probability of choosing 2 rare cards from a bin of 100 trading cards (consisting of 5 rare cards, 35 limited cards, and 60 common cards) without replacement, you would calculate it as follows:
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Choosing the first rare card: There are 5 rare cards out of 100 total cards, so the probability of choosing the first rare card is:
\[ P(\text{first rare card}) = \frac{5}{100} \]
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Choosing the second rare card: After choosing the first rare card, there will be 4 rare cards left out of a total of 99 cards (because we are not replacing the first card). So, the probability of choosing the second rare card is:
\[ P(\text{second rare card | first rare card}) = \frac{4}{99} \]
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Overall probability of choosing 2 rare cards: The overall probability is the product of the probabilities of each event occurring:
\[ P(\text{2 rare cards}) = P(\text{first rare card}) \times P(\text{second rare card | first rare card}) = \frac{5}{100} \times \frac{4}{99} \]
Thus, the correct interpretation of the probability of choosing 2 rare cards from the bin (without replacement) is:
\[ \frac{5}{100} \cdot \frac{4}{99} \]
Based on the options you provided, this calculation leads us to conclude that none of the given responses match this reasoning precisely, but the option that correctly represents the probability of choosing the first rare card is:
\[ \frac{5}{100} \]
However, if we're focusing on the aspect of probabilities being multiplied for both rare cards, the correct interpretation is the multiplication of probabilities. Although none of the choices you provided accurately depicts the full calculation, the response that denotes multiplication (which is the closest we can get) is likely aimed to reflect the first probability (5/100).
In summary, the best choice among the provided responses would be:
\(\frac{5}{100} \cdot \frac{4}{99}\) (not explicitly listed but understood conceptually). If seeking to choose from what's available, focus on the first part—\(\frac{5}{100}\)—indicating the start of the probability sequence for one rare card.