Quiz
The Shuffled Color Odds
Imagine you have a deck of cards consisting of 25 red cards and 25 black cards. You sit down at a table and thoroughly shuffle them. You draw the first two cards off the top of the deck.
What are the odds that both cards you pulled are of the same color?
Your brain wants to assume every card draw is independent, like a coin flip. But when you draw the first card, you are changing the composition of the deck for the second draw. Think about what is left in the deck after card number one.
The correct answer is 2: Slightly less than 50% (exactly 24/49 or ~48.98%).
This is a classic trap where human intuition defaults to an independent 50/50 state. Let’s look at the math from first principles:
- It doesn’t matter what color the first card is. Let’s assume it’s Red.
- Once that first Red card is out of the deck, there are now only 49 cards remaining in total.
- Within those remaining 49 cards, there are 24 Red cards left and 25 Black cards left.
- Therefore, the probability that the second card matches the first one is $\frac{24}{49}$, which is $\approx 48.98\%$.
Because drawing the first card reduces the pool of its own color, the matching color is always at a slight mathematical disadvantage!