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.