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.(1 point)
Responses

5100
Start Fraction 5 over 100 End Fraction

5100⋅499
Start Fraction 5 over 100 End Fraction times Start Fraction 4 over 99 End Fraction

5100+5100
Start Fraction 5 over 100 End Fraction times Start Fraction 5 over 100 End Fraction

5100⋅5100
Start Fraction 5 over 100 End Fraction times Start Fraction 5 over 100 End Fraction

Answer 1

To find the probability of choosing 2 rare cards from the bin without replacement, we need to consider the probability of drawing the first rare card and then the probability of drawing a second rare card after the first one has already been drawn.

1. The probability of drawing the first rare card is \( \frac{5}{100} \) (since there are 5 rare cards out of 100 total cards).
2. After drawing one rare card, there are now 4 rare cards left and 99 total cards. The probability of drawing a second rare card is \( \frac{4}{99} \).

Therefore, the probability of choosing 2 rare cards is:
\[
\frac{5}{100} \times \frac{4}{99}
\]

This corresponds to the choice:
\[
\frac{5}{100} \cdot \frac{4}{99}
\]

So the correct interpretation of the probability is:
\[
\frac{5}{100} \cdot \frac{4}{99}
\]

Thus, the answer is:
**5100⋅499**
\[ \text{Start Fraction } \frac{5}{100} \text{ End Fraction times Start Fraction } \frac{4}{99} \text{ End Fraction} \]