Question

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.

A. 5/100 ⋅ 4/99
B. 5/100
C. 5/100 ⋅ 5/100
D. 5/100 + 5/100

Answer 1

To calculate the probability of choosing 2 rare cards from the bin without replacement, we can approach it step by step.

1. **Probability of choosing the first rare card**: There are 5 rare cards out of 100 total cards, so the probability of picking a rare card first is:
\[
\frac{5}{100}
\]

2. **Probability of choosing the second rare card**: After picking one rare card, there are now 4 rare cards left and only 99 total cards left (since one card has already been chosen). Thus, the probability of picking a second rare card is:
\[
\frac{4}{99}
\]

3. **Total probability of picking 2 rare cards**: To find the total probability of both events happening (choosing a rare card first and then choosing another rare card), we multiply the probabilities:
\[
\frac{5}{100} \cdot \frac{4}{99}
\]

Therefore, the correct interpretation of the probability of choosing 2 rare cards from the bin without replacement is:

**A. 5/100 ⋅ 4/99**.