Have you ever wondered how to calculate the odds of drawing a specific card when you have more than 100% chance of getting it? I know I have. Recently, I stumbled upon a Reddit post that got me thinking about this very problem. The original poster was trying to figure out the chances of completing a set of 40 Disney cards with 120 unopened cards. It sounds simple, but the math gets tricky when you go beyond 100%.
The issue arises because our intuition tells us that once we have 40 cards, we should have a 100% chance of getting an individual card. But that’s not the case. The probability of getting a specific card doesn’t quite work that way. So, how do we calculate the odds when we have more than 100%?
To understand this, let’s break down the problem step by step. Assume there’s an even distribution of cards, which means each card has an equal chance of being drawn. When you have 20 cards, it’s logical to assume you have a 50% chance of getting an individual card. But as you collect more cards, the probability of getting that specific card increases. The question is, how do we quantify that increase?
The key is to think about the number of cards you need to complete the set, not just the number of cards you have. In this case, you need 40 cards to complete the set. So, even if you have 120 cards, you still don’t have a 100% chance of getting every individual card. The probability of getting a specific card is still less than 100%.
To calculate the odds, you can use the hypergeometric distribution formula. It’s a bit complex, but it gives you the probability of getting exactly k successes (in this case, getting a specific card) in n draws (the number of cards you have) from a population of N items (the total number of cards in the set).
While the math can be daunting, understanding the concept is essential. It’s not just about calculating the odds; it’s about grasping the underlying principles of probability. So, the next time you’re collecting cards or trying to complete a set, remember that the probability of getting a specific card is not always as simple as it seems.
What do you think? Have you ever struggled with calculating probabilities in similar situations? Share your thoughts in the comments!