Definition: A compound event is an event made of two or more simple events, such as flipping a coin and rolling a die together.
What is a compound event?
It combines several simple events, like drawing two cards or spinning a spinner twice.
How do you find its probability?
Count the outcomes in the sample space that match, and divide by the total. For independent events, you can also multiply probabilities.
What does an example look like?
Mathbot spins a spinner with 5 equal sections numbered 1 to 5, then flips a coin. What is the chance of an odd number and tails?
- P(odd) = 3/5
- P(tails) = 1/2
- Both: 3/5 x 1/2 = 3/10
Counting agrees: there are 10 outcomes, and 3 are favorable (1T, 3T, 5T).
What if the events depend on each other?
Drawing without replacement changes the odds. From a bag with 4 red and 6 blue marbles, the chance of two reds is 4/10 x 3/9 = 12/90 = 2/15.
What is a common mistake?
Adding where multiplication is needed. For both events happening in sequence, multiply. Also, when the first draw is not put back, the second probability changes.