What is the probability of drawing a red card and then a black card without replacement?

The probability of drawing a red card and then a black card without replacement is 26/102 or approximately 0.255.

To understand this, let's break it down step by step. A standard deck of cards has 52 cards, with 26 red cards (hearts and diamonds) and 26 black cards (clubs and spades). When you draw the first card, there are 26 red cards out of 52, so the probability of drawing a red card first is 26/52, which simplifies to 1/2 or 0.5.

After drawing a red card, there are now 51 cards left in the deck, with 25 of them being red and 26 being black. Now, you want to draw a black card. The probability of drawing a black card from the remaining 51 cards is 26/51.

To find the combined probability of both events happening (drawing a red card first and then a black card), you multiply the probabilities of each individual event. So, you multiply the probability of drawing a red card (1/2) by the probability of drawing a black card after a red card (26/51):

(1/2) * (26/51) = 26/102.

This fraction can be simplified to 13/51, which is approximately 0.255 when converted to a decimal. This means there is about a 25.5% chance of drawing a red card followed by a black card without replacement.