1. Let's start by understanding what probability is. Probability measures how likely an event is to happen. It is a number between 0 and 1, where 0 means the event will not happen and 1 means it will definitely happen. 2. The formula for probability of an event $E$ is: $$P(E) = \frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}}$$ 3. Important rules: - The sum of probabilities of all possible outcomes of an experiment is 1. - Probability of an impossible event is 0. - Probability of a certain event is 1. 4. Example question a teacher might ask: "What is the probability of rolling a 3 on a fair six-sided die?" 5. Solution: - Total possible outcomes when rolling a die = 6 (numbers 1 to 6). - Favorable outcomes for rolling a 3 = 1 (only the number 3). - Using the formula: $$P(3) = \frac{1}{6}$$ 6. Explanation: Since there is only one side with a 3 and six sides total, the chance of getting a 3 is one out of six. 7. Another common question: "What is the probability of getting an even number on a die?" 8. Solution: - Even numbers on a die: 2, 4, 6 (3 favorable outcomes). - Total outcomes: 6. - Probability: $$P(\text{even}) = \frac{3}{6} = \frac{1}{2}$$ 9. This means there is a 50% chance to roll an even number. 10. Probability helps us predict outcomes in uncertain situations by quantifying likelihoods.