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+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

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

5100
Start Fraction 5 over 100 End Fraction
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Answer 1

To find the probability of choosing 2 rare cards from a bin of 100 trading cards without replacement, we need to calculate the probability of drawing a rare card on the first draw and then on the second draw.

1. The probability of drawing the first rare card is \( \frac{5}{100} \) (as there are 5 rare cards out of 100 total cards).

2. After drawing one rare card, there are now 4 rare cards left out of a total of 99 cards, so the probability of drawing a rare card on the second draw is \( \frac{4}{99} \).

Therefore, the combined probability of drawing 2 rare cards without replacement is:

\[
\frac{5}{100} \times \frac{4}{99}
\]

So, the correct answer is:

\[
\frac{5}{100} \times \frac{4}{99}
\]

This interpretation matches the option:

\[
\frac{5}{100} \cdot \frac{4}{99}
\]

Thus, the correct interpretation from the choices given is:

**\( \frac{5}{100} \cdot \frac{4}{99} \)**.