1. Stating the problem: Let's explore some fundamental probability examples to understand basic concepts. 2. Example 1: Probability of drawing an ace from a standard deck of 52 cards. There are 4 aces in the deck. Probability = $\frac{\text{number of favorable outcomes}}{\text{total number of outcomes}} = \frac{4}{52} = \frac{1}{13}$. 3. Example 2: Probability of rolling an even number on a fair six-sided die. Even numbers on a die are 2, 4, and 6, so 3 favorable outcomes. Probability = $\frac{3}{6} = \frac{1}{2}$. 4. Example 3: Probability of flipping two coins and getting exactly one head. Possible outcomes: HH, HT, TH, TT. Favorable outcomes with exactly one head are HT and TH. Probability = $\frac{2}{4} = \frac{1}{2}$. 5. Example 4: If a bag has 3 red and 2 blue balls, what's the probability of randomly picking a red ball? Total balls = 3 + 2 = 5. Probability of red = $\frac{3}{5}$. These simple examples demonstrate key ideas of probability by calculating favorable outcomes over total outcomes.