Independent events
Calculate probability of independent events in Grade 9 math by multiplying individual probabilities: P(A and B)=P(A)×P(B), since one event's outcome does not affect the other.
Key Concepts
Property The outcome of the first event does not affect the second event. The probability is calculated as $P(A \text{ and } B) = P(A) \cdot P(B)$.
Examples Rolling a 5 on a die and flipping heads: $P(5 \text{ and heads}) = \frac{1}{6} \cdot \frac{1}{2} = \frac{1}{12}$. Drawing a card, replacing it, then drawing another: $P(\text{King and then Queen}) = \frac{4}{52} \cdot \frac{4}{52} = \frac{1}{169}$. A spinner with 8 sectors is spun twice: $P(\text{red and then blue}) = \frac{1}{8} \cdot \frac{1}{8} = \frac{1}{64}$.
Explanation Think of this as totally separate actions, like flipping a coin and then rolling a die. What happens first has zero impact on what happens next! To find the combined chance of both happening, you simply multiply their individual probabilities together. It’s like a probability team up where each member acts alone.
Common Questions
What are independent events in probability?
Two events are independent if the occurrence of one does not change the probability of the other. Flipping a coin and rolling a die are independent — the coin result has no influence on the die result.
What is the multiplication rule for independent events?
For independent events A and B, P(A and B) = P(A) × P(B). For example, the probability of flipping Heads (1/2) and rolling a 4 (1/6) is (1/2) × (1/6) = 1/12.
How do independent events differ from dependent events?
With independent events the probability of the second event stays the same regardless of the first outcome. With dependent events the first outcome changes the available options, altering the probability of the second event.