Two cards are drawn from a standard deck without replacement. What is the probability that the first card is a spade and the second card is red? (Round your answer to three decimal places.)

We are asked to find the probability of two specific events when drawing two cards from a standard deck of 52 cards, without replacement:

1. The first card drawn is a spade.
2. The second card drawn is red (either a heart or a diamond).

### Step 1: Determine the number of spades
There are 13 spades in a standard deck of 52 cards.

### Step 2: Calculate the probability of drawing a spade first
Since there are 13 spades out of 52 cards, the probability of drawing a spade on the first draw is:
\[
P(\text{Spade on 1st draw}) = \frac{13}{52} = \frac{1}{4}
\]

### Step 3: Calculate the probability of drawing a red card second
After drawing a spade, 51 cards remain, and since the first card was a spade, all 26 red cards (13 hearts + 13 diamonds) are still in the deck. The probability of drawing a red card on the second draw is:
\[
P(\text{Red on 2nd draw}) = \frac{26}{51}
\]

### Step 4: Multiply the probabilities
Since the events are dependent (the second draw is affected by the first), the total probability is the product of the two probabilities:
\[
P(\text{Spade on 1st and Red on 2nd}) = \frac{13}{52} \times \frac{26}{51}
\]

Let's calculate this:
\[
P = \frac{13}{52} \times \frac{26}{51} = \frac{1}{4} \times \frac{26}{51} = \frac{26}{204} \approx 0.127
\]

Thus, the probability that the first card is a spade and the second card is red is approximately **0.127**.

Do you want more details or have any questions?

Here are five related questions to expand on this:
1. What is the probability that both cards drawn are spades?
2. What is the probability of drawing two red cards consecutively?
3. What is the probability of drawing a black card first and a red card second?
4. How does the probability change if the cards are drawn with replacement?
5. What is the probability that neither card drawn is a face card?

**Tip**: When calculating probabilities of multiple events, always check if the events are independent or dependent before multiplying the probabilities.

Discover how to calculate the probability of drawing a spade first and a red card second from a standard deck of cards without replacement. This problem covers key concepts in probability, including dependent events and combinatorics. The solution involves multiplying probabilities and is suitable for students in Grades 9-12.

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