Probability of Independent Events
Calculate the probability of independent events in Grade 10 probability. Multiply individual probabilities P(A)×P(B) to find joint probability when events do not influence each other.
Key Concepts
For the probability of two independent events A and B: $$P(A \text{ and } B) = P(A) \cdot P(B)$$.
A coin is flipped and a die is rolled. Find the probability of getting heads and rolling a 4. $$P(\text{heads and 4}) = P(\text{heads}) \cdot P(4) = \frac{1}{2} \cdot \frac{1}{6} = \frac{1}{12}$$ A bag contains 3 red and 7 blue marbles. A marble is drawn and replaced. Find P(red then blue). $$P(\text{red then blue}) = P(\text{red}) \cdot P(\text{blue}) = \frac{3}{10} \cdot \frac{7}{10} = \frac{21}{100}$$.
Imagine flipping a coin and then rolling a die. The coin doesn't care what the die does, and vice versa! These are independent events—one doesn't affect the other's outcome. To find the chance of both happening in a sequence, you just multiply their individual probabilities. Think of it as finding a fraction of a fraction.
Common Questions
What is the multiplication rule for independent events?
P(A and B) = P(A) × P(B). For two independent events, multiply their probabilities. For example, P(rolling 3 and flipping heads) = (1/6) × (1/2) = 1/12.
How do you check if two events are independent?
Events A and B are independent if P(A|B) = P(A) — knowing B occurred does not change the probability of A. Equivalently, P(A and B) = P(A) × P(B) must hold.
How do you extend the multiplication rule to three or more independent events?
P(A and B and C) = P(A) × P(B) × P(C). Multiply all individual probabilities together. Each additional independent event multiplies the joint probability by its own probability.