To find the probability of choosing 2 rare cards from the bin without replacement, you need to consider the probability of selecting the first rare card and then the probability of selecting a second rare card after the first one has been removed.
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The probability of choosing the first rare card: \[ \text{P(1st rare)} = \frac{5}{100} \]
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After choosing one rare card, there are now 4 rare cards left and only 99 cards remaining in total. The probability of choosing the second rare card is: \[ \text{P(2nd rare | 1st rare)} = \frac{4}{99} \]
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Therefore, the combined probability of choosing 2 rare cards in succession is: \[ \text{P(2 rare)} = \frac{5}{100} \times \frac{4}{99} \]
This corresponds to the following option: \[ \frac{5}{100} \cdot \frac{4}{99} \] Thus, the correct interpretation of the probability of choosing 2 rare cards from the bin is: \[ \frac{5}{100} \cdot \frac{4}{99} \]
Therefore, the correct response is: \[ \frac{5}{100} \cdot \frac{4}{99} \] (which is not explicitly listed in your options but matches with the calculation provided). If you are looking for the closest option in your original list, it would be: \[ \frac{5}{100} \cdot \frac{4}{99} \] (if available). If not, there seems to be a mismatch in the options given.
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