What did the teacher say about independent probability?

Independent probability refers to the concept in probability theory where the occurrence of one event does not affect the occurrence of another event. Here are the key points typically discussed regarding independent probability: 1. **Definition**: Two events, A and B, are independent if the probability of both events occurring together is equal to the product of their individual probabilities. Mathematically, this is expressed as: \[ P(A \cap B) = P(A) \times P(B) \] 2. **Example**: If you flip a coin and roll a die, the outcome of the coin flip (heads or tails) does not affect the outcome of the die roll (1 through 6). Therefore, these two events are independent. 3. **Calculation**: To determine if two events are independent, you can calculate their probabilities and check if the above equation holds true. 4. **Applications**: Understanding independent events is crucial in various fields, including statistics, finance, and risk assessment, as it helps in making predictions and decisions based on the likelihood of different outcomes. 5. **Complementary Events**: It's also important to note that if two events are independent, their complements are also independent. For example, if A is independent of B, then the event "not A" is independent of B as well. These points summarize the concept of independent probability as typically discussed in educational settings.