What is the probability of drawing two black cards in a row without replacement?

The probability of drawing two black cards in a row without replacement is 25/102.

To understand this, let's break it down step by step. A standard deck of cards has 52 cards in total, with 26 black cards (13 spades and 13 clubs) and 26 red cards (13 hearts and 13 diamonds). When you draw the first card, the probability of it being black is 26 out of 52, which simplifies to 1/2 or 50%.

Once you've drawn the first black card, there are now 51 cards left in the deck, with 25 of them being black. The probability of drawing a second black card is then 25 out of 51.

To find the combined probability of both events happening (drawing a black card first and then another black card), you multiply the probabilities of each individual event. So, you multiply 26/52 by 25/51.

Here's the calculation:
\[ \frac{26}{52} \times \frac{25}{51} = \frac{1}{2} \times \frac{25}{51} = \frac{25}{102} \]

So, the probability of drawing two black cards in a row without replacement is 25/102, which is approximately 0.245 or 24.5%. This means that if you were to repeat this process many times, you would expect to draw two black cards in a row about 24.5% of the time.