6:34PM Thu Jan 23
In Emilio Mejia Felici… AA. 12 Independence and conditional probability
If and are independent events, what is the probability that and both occur?
Simplify any fractions.

When two events and are independent, the probability of both events occurring is calculated by multiplying their individual probabilities. So, if the probability of event occurring is and the probability of event occurring is , then the probability of both events occurring is given by .

For instance, if and , the combined probability is . So, the answer you would put in the box is after simplification.

Understanding independent events can be quite fun! In real-world examples, consider flipping a coin and rolling a die. The coin landing heads (event ) is independent of the die rolling a four (event ). This illustrates how events can happen without influencing each other, making probability calculations simpler and more intuitive!