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$Suppose two cards are drawn randomly. What is the probability of drawing two green cards, if the first card is NOT replaced before the second draw? Assume the first card drawn is green. Show your answer as a fraction in lowest terms. Enter the numerator. Enter Copyright 93003 - 2024 International Academy of Science. All Rights Resenved$

Suppose two cards are drawn randomly. $\newline$ What is the probability of drawing two green cards, if the first card is NOT replaced before the second draw? Assume the first card drawn is green. $\newline$ Show your answer as a fraction in lowest terms. Enter the numerator. $\newline$ Enter $\newline$ Copyright $93003$ - $2024$ International Academy of Science. All Rights Resenved

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Find limits involving factorization and rationalization

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Q. Suppose two cards are drawn randomly.

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What is the probability of drawing two green cards, if the first card is NOT replaced before the second draw? Assume the first card drawn is green.

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Show your answer as a fraction in lowest terms. Enter the numerator.

\newline

Enter

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93003

2024

International Academy of Science. All Rights Resenved

Determine Total Green Cards: Determine the total number of green cards initially. $\newline$ Assuming we have a standard deck and that ＂green cards＂ refers to a specific subset of that deck, we need to know the total number of green cards. Since the problem does not specify the number of green cards, we will denote this number as $G$ .
Calculate First Card Probability: Calculate the probability of drawing the first green card. $\newline$ Since the first card drawn is green, the probability of this event is $1$ , because it is given that the first card is green. $\newline$ $P(\text{first card is green}) = 1$
Calculate Second Card Probability: Calculate the probability of drawing the second green card after the first green card has been drawn and not replaced. $\newline$ After drawing the first green card, there are now $(G - 1)$ green cards left in the deck. The total number of cards in the deck is also reduced by $1$ , so if the deck originally had $N$ cards, there are now $(N - 1)$ cards left. $\newline$ The probability of drawing a second green card is therefore: $\newline$ $P(\text{second card is green} | \text{first card is green}) = \frac{(G - 1)}{(N - 1)}$
Calculate Combined Probability: Calculate the combined probability of both events happening in succession. $\newline$ Since the first event (drawing a green card) is certain, we only need to consider the probability of the second event. The combined probability is the product of the probabilities of the two events: $\newline$ $P(\text{two green cards in succession}) = P(\text{first card is green}) \times P(\text{second card is green | first card is green})$ $\newline$ $P(\text{two green cards in succession}) = 1 \times (G - 1) / (N - 1)$ $\newline$ $P(\text{two green cards in succession}) = (G - 1) / (N - 1)$
Express Probability in Lowest Terms: Express the probability in lowest terms and find the numerator. $\newline$ To express the probability in lowest terms, we would need to simplify the fraction $(G - 1) / (N - 1)$ . However, without specific values for $G$ and $N$ , we cannot simplify further or find the numerator. The problem statement does not provide the total number of cards or the number of green cards, so we cannot complete this step accurately.