Independent and Dependent Events
Distinguish independent and dependent events in Grade 10 probability. Determine whether one event affects another and apply the correct multiplication rule to calculate joint probabilities.
Key Concepts
Two events are independent if the probability of one event is not affected by whether or not the other event occurs. Two events are dependent if the probability of one event is affected by whether or not the other event occurs.
Independent: Flipping a coin and then rolling a die. The coin's outcome ($H$ or $T$) has no effect on the die's outcome (1 6). Dependent: Drawing a card from a deck, not replacing it, and then drawing another. The first card drawn changes the remaining deck. Independent: Picking a marble from a bag, putting it back, then picking another. The odds reset for the second pick.
Common Questions
What is the difference between independent and dependent events?
Independent events do not affect each other — P(A|B) = P(A). Dependent events do affect each other — the occurrence of one changes the probability of the other.
How do you calculate the probability of two independent events both occurring?
Multiply their individual probabilities: P(A and B) = P(A) × P(B). For example, flipping heads twice: P(H) × P(H) = 0.5 × 0.5 = 0.25.
How do you calculate probability for dependent events?
Use P(A and B) = P(A) × P(B|A), where P(B|A) is the conditional probability of B given A already occurred. For example, drawing cards without replacement.