How do you calculate the probability of two independent events occurring?

To calculate the probability of two independent events occurring, multiply the probabilities of each event together.

When dealing with probabilities, an independent event is one where the outcome of one event does not affect the outcome of another. For example, flipping a coin and rolling a die are independent events because the result of the coin flip does not influence the result of the die roll.

Let's say you have two independent events, A and B. The probability of event A occurring is denoted as P(A), and the probability of event B occurring is denoted as P(B). To find the probability of both events A and B occurring, you simply multiply their individual probabilities: P(A and B) = P(A) × P(B).

For instance, if the probability of flipping a coin and getting heads (event A) is 0.5, and the probability of rolling a die and getting a 4 (event B) is 1/6, then the probability of both events happening together is:
P(A and B) = P(A) × P(B) = 0.5 × 1/6 = 0.5/6 = 1/12 ≈ 0.0833.

This means there is approximately an 8.33% chance of both flipping heads and rolling a 4. Remember, this method only works for independent events. If the events are not independent, you would need to use a different approach to calculate the combined probability.