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
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
Responses
5100+5100
Start Fraction 5 over 100 End Fraction times Start Fraction 5 over 100 End Fraction
5100
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
Answers
GPT-4o mini
To find the probability of choosing 2 rare cards from the bin without replacement, we can calculate it step by step.
1. The probability of drawing the first rare card is \( \frac{5}{100} \).
2. After drawing one rare card, there are now 4 rare cards left and a total of 99 cards remaining. Therefore, the probability of drawing a second rare card is \( \frac{4}{99} \).
Now, we multiply these probabilities together:
\[
P(\text{2 rare cards}) = \frac{5}{100} \times \frac{4}{99}
\]
This can be represented as:
\[
P(\text{2 rare cards}) = \frac{5}{100} \cdot \frac{4}{99}
\]
The given options need to be checked against this calculation. The probability of choosing 2 rare cards from the bin is thus:
- \( \frac{5}{100} \cdot \frac{4}{99} \)
However, your selections only include options with \( \frac{5}{100} \) or those multiplied incorrectly.
Out of the options given, \( \frac{5}{100} \cdot \frac{4}{99} \) is the correct approach, but neither of the provided answers directly states this exact multiplication.
If the interpretation should represent just the first choice, without explicitly calculating the second draw, the option that represents grabbing one rare card with the understanding that we would follow it up by another rare card would be:
**\( \frac{5}{100} \cdot \frac{4}{99} \)**
Since none of the provided options reflect this correctly, it seems there may be an error in the answer choices listed. The most relevant response from the options provided is:
**\( \frac{5}{100} \cdot \frac{499}{100} \)**
This does not directly relate to the calculations for the second draw and should be clarified. Therefore, please note that the correct approach is indeed:
**\( \frac{5}{100} \cdot \frac{4}{99} \)**.
1. The probability of drawing the first rare card is \( \frac{5}{100} \).
2. After drawing one rare card, there are now 4 rare cards left and a total of 99 cards remaining. Therefore, the probability of drawing a second rare card is \( \frac{4}{99} \).
Now, we multiply these probabilities together:
\[
P(\text{2 rare cards}) = \frac{5}{100} \times \frac{4}{99}
\]
This can be represented as:
\[
P(\text{2 rare cards}) = \frac{5}{100} \cdot \frac{4}{99}
\]
The given options need to be checked against this calculation. The probability of choosing 2 rare cards from the bin is thus:
- \( \frac{5}{100} \cdot \frac{4}{99} \)
However, your selections only include options with \( \frac{5}{100} \) or those multiplied incorrectly.
Out of the options given, \( \frac{5}{100} \cdot \frac{4}{99} \) is the correct approach, but neither of the provided answers directly states this exact multiplication.
If the interpretation should represent just the first choice, without explicitly calculating the second draw, the option that represents grabbing one rare card with the understanding that we would follow it up by another rare card would be:
**\( \frac{5}{100} \cdot \frac{4}{99} \)**
Since none of the provided options reflect this correctly, it seems there may be an error in the answer choices listed. The most relevant response from the options provided is:
**\( \frac{5}{100} \cdot \frac{499}{100} \)**
This does not directly relate to the calculations for the second draw and should be clarified. Therefore, please note that the correct approach is indeed:
**\( \frac{5}{100} \cdot \frac{4}{99} \)**.