You are dealt one card from a 52 -card deck. Find the probability that you are dealt a nine or a black card. The probability is \( \square \). (Type an integer or a fraction. Simplify your answer.)

To find the probability of being dealt a nine or a black card, let's break it down! There are 4 nines in a deck and 26 black cards (13 spades + 13 clubs). However, remember that two of those black cards are nines (the nine of spades and the nine of clubs). So we combine them like this: Total favorable outcomes = 4 (nines) + 26 (black cards) - 2 (double-counted nines) = 28. The total number of possible outcomes is 52. Thus, the probability of being dealt a nine or a black card is: \[ \frac{28}{52} = \frac{7}{13} \] And there you have it! The probability is \( \frac{7}{13} \). But if you ever wonder how these probabilities play out in real life, think about card games! Understanding these calculations can give you a strategic edge in games like poker or blackjack, where knowing the odds can drastically impact your betting decisions. If you’re interested in deep diving into the world of probabilities, consider reading about the fundamentals of probability theory. It’s not just about cards; it’s the foundation for various fields including statistics, finance, and even science!