To find the probability of choosing 2 rare cards from the bin without replacement, you need to consider the two stages of drawing the cards:
- The probability of drawing the first rare card from the 5 rare cards out of the total 100 cards.
- Once the first rare card is drawn, there are now 4 rare cards left and a total of 99 cards remaining, so you need to find the probability of drawing a second rare card.
The probability of drawing the first rare card is: \[ \frac{5}{100} \]
After drawing the first rare card, the updated probabilities are:
- Rare cards left: 4
- Total cards left: 99
So, the probability of drawing the second rare card is: \[ \frac{4}{99} \]
Now, to find the combined probability of both events occurring (drawing the first rare card and then drawing the second rare card), you multiply the two probabilities: \[ P(\text{2 rare cards}) = \frac{5}{100} \times \frac{4}{99} \]
So the correct interpretation of the probability of choosing 2 rare cards from the bin is: \[ \frac{5}{100} \times \frac{4}{99} \]
None of the provided options match this exactly, but the first response seems to be formatted incorrectly, as it likely intended to convey this same multiplication. So the correct answer is: \[ \frac{5}{100} \times \frac{4}{99} \]