Compound events
Compound events involve two or more independent events happening together. To find the probability that both events occur, multiply their individual probabilities: P(A and B) = P(A) × P(B). This works when the events are independent — meaning the outcome of one does not affect the other. For example, the probability of flipping heads and rolling a 3 is P(heads) × P(3) = 1/2 × 1/6 = 1/12. This 7th grade math concept is covered in Saxon Math, Course 2, and builds on simple probability toward an understanding of combined likelihoods.
Key Concepts
Property To find the probability of two or more independent events occurring, multiply the probabilities of each event: $P(A \text{ and } B) = P(A) \cdot P(B)$.
Examples What is the probability of flipping tails and rolling a 5 on a number cube? $P(\text{Tails and 5}) = P(\text{Tails}) \cdot P(5) = \frac{1}{2} \cdot \frac{1}{6} = \frac{1}{12}$ What is the probability of flipping tails three times in a row? $P(\text{Tails, Tails, Tails}) = \frac{1}{2} \cdot \frac{1}{2} \cdot \frac{1}{2} = \frac{1}{8}$.
Explanation This is like a video game combo! To land the full attack, you have to succeed at each button press. We multiply the probability of each individual move to find the chance of pulling off that epic final combo. Each event must happen for the compound event to succeed.
Common Questions
What are compound events in probability?
Compound events involve two or more simple events happening together. ‘Flipping a coin and rolling a die’ is a compound event. You find the probability by multiplying the individual probabilities if the events are independent.
How do you calculate the probability of compound events?
Multiply the probabilities of each individual event: P(A and B) = P(A) × P(B). For example, P(rolling a 4) = 1/6, and P(flipping heads) = 1/2, so P(both) = 1/6 × 1/2 = 1/12.
What does independent mean in probability?
Two events are independent if the outcome of one does not affect the outcome of the other. Flipping a coin and rolling a die are independent because the coin result doesn’t change the die result.
What is the difference between simple and compound events?
A simple event has one outcome (rolling a 3). A compound event involves two or more outcomes occurring together (rolling a 3 AND flipping heads).
What is the probability of rolling two sixes in a row?
P(6) on one die = 1/6. For two rolls: P(6 and 6) = 1/6 × 1/6 = 1/36.
When do students learn about compound events?
Compound events in probability are introduced in 7th grade math as an extension of simple probability.
Which textbook covers compound events?
Saxon Math, Course 2 covers compound events and independent probability.