There are 100 trading cards in a bin. They include 5 rare cards, 35 limited cards, and the remainder are common cards. Which of the following correctly interprets the probability of choosing 2 rare cards from the bin? Assume that the cards are pulled without replacement.

Answer 1

To determine the probability of choosing 2 rare cards from a bin containing 100 trading cards (5 rare, 35 limited, and the rest common), we start by calculating the total number of cards and the individual card counts.

1. Count the cards:

   • Total cards = 100
   • Rare cards = 5
   • Limited cards = 35
   • Common cards = 100 - 5 - 35 = 60

2. The event is drawing 2 rare cards without replacement.

3. To find the probability of this event, we can use the formula for the probability of two dependent events. The probability of drawing the first rare card is given by the ratio of rare cards to total cards, and then the probability of drawing the second rare card is the ratio of the remaining rare cards to the remaining total cards after drawing the first.

4. The calculation is as follows:

   • Probability of drawing the first rare card = \( \frac{5}{100} \)
   • After drawing one rare card, there are now 4 rare cards left and 99 cards total.
   • Probability of drawing the second rare card = \( \frac{4}{99} \)

5. The overall probability of drawing two rare cards is calculated by multiplying these probabilities: \[ P(\text{2 rare cards}) = P(\text{1st rare}) \times P(\text{2nd rare}) = \frac{5}{100} \times \frac{4}{99} = \frac{20}{9900} = \frac{2}{990} = \frac{1}{495} \]

Thus, the probability of choosing 2 rare cards from the bin, without replacement, is \( \frac{1}{495} \).