To determine the correct probability of choosing 2 rare cards from a bin of 100 cards (which contains 5 rare cards) without replacement, we need to calculate the probability of drawing one rare card and then another rare card after the first has been drawn.
-
The probability of drawing the first rare card is the number of rare cards divided by the total number of cards: \[ P(\text{1st rare}) = \frac{5}{100} \]
-
After drawing one rare card, there are now 4 rare cards left and only 99 cards total remaining. Thus, the probability of drawing a second rare card is: \[ P(\text{2nd rare | 1st rare}) = \frac{4}{99} \]
-
The probability of both events happening (drawing both cards) is the product of the probabilities: \[ P(\text{2 rare}) = P(\text{1st rare}) \times P(\text{2nd rare | 1st rare}) = \left(\frac{5}{100}\right) \times \left(\frac{4}{99}\right) \]
Thus, the correct interpretation of the probability of choosing 2 rare cards from the bin is: \[ \frac{5}{100} \times \frac{4}{99} \] This corresponds to the option:
\(\frac{5}{100} \times \frac{4}{99}\).