Suppose that events E and F are independent, P(E) = 0.3 and P(F) = 0.6. What is the P(E and F)?

Verified step by step guidance

1. Recall the definition of independent events: two events E and F are independent if the occurrence of one does not affect the probability of the other.
2. For independent events, the probability of both events occurring together (E and F) is the product of their individual probabilities.
3. Write the formula for the probability of both events happening: \(P(E \text{ and } F) = P(E) \times P(F)\).
4. Substitute the given probabilities into the formula: \(P(E \text{ and } F) = 0.3 \times 0.6\).
5. Multiply the values to find \(P(E \text{ and } F)\), which gives the probability of both events occurring simultaneously.

Key Concepts

Independent Events

Two events are independent if the occurrence of one does not affect the probability of the other. This means that knowing one event happened does not change the likelihood of the other event occurring.

Probability of an Event

The probability of an event is a measure between 0 and 1 that quantifies the likelihood of that event occurring. For example, P(E) = 0.3 means event E has a 30% chance of happening.

Multiplication Rule for Independent Events

If two events are independent, the probability that both occur (E and F) is the product of their individual probabilities: P(E and F) = P(E) × P(F). This rule simplifies calculating joint probabilities for independent events.