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⋅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 5100
Answers
GPT-4o mini
To find the probability of selecting 2 rare cards from the bin without replacement, we can use the following reasoning:
1. The total number of cards is 100.
2. There are 5 rare cards.
3. When you pick the first rare card, the probability of this happening is \(\frac{5}{100}\).
4. After pulling one rare card, there are now 99 cards left in the bin, and only 4 rare cards remaining. Therefore, the probability of picking a second rare card is \(\frac{4}{99}\).
Thus, the probability of choosing 2 rare cards in sequence without replacement is:
\[
\text{Probability} = \left(\frac{5}{100}\right) \times \left(\frac{4}{99}\right)
\]
So the correct interpretation of the probability of choosing 2 rare cards from the bin is:
\(\frac{5}{100} \times \frac{4}{99}\)
This corresponds to the first option in your list.
1. The total number of cards is 100.
2. There are 5 rare cards.
3. When you pick the first rare card, the probability of this happening is \(\frac{5}{100}\).
4. After pulling one rare card, there are now 99 cards left in the bin, and only 4 rare cards remaining. Therefore, the probability of picking a second rare card is \(\frac{4}{99}\).
Thus, the probability of choosing 2 rare cards in sequence without replacement is:
\[
\text{Probability} = \left(\frac{5}{100}\right) \times \left(\frac{4}{99}\right)
\]
So the correct interpretation of the probability of choosing 2 rare cards from the bin is:
\(\frac{5}{100} \times \frac{4}{99}\)
This corresponds to the first option in your list.