Compound Event
A compound event in probability is an event that contains more than one outcome from the sample space of a random experiment. Unlike an elementary event which has only a single outcome, a compound event is formed by combining two or more elementary events.
Key Concepts
A compound event represents a collection of multiple favorable outcomes that satisfy a specific condition.
It can occur in a single trial, such as rolling an even number on one die, or across multiple trials, such as getting two heads when tossing two coins.
The probability of a compound event is calculated by adding the probabilities of all the individual elementary events that make up the compound event.
Formula & Equation
P(E) represents the probability of the compound event E.
Common Misconceptions
Myth: Compound events only occur when you perform multiple experiments at the same time, like rolling two dice or tossing three coins.
Fact: A compound event can happen in a single experiment. For example, rolling a number greater than 4 on a single die is a compound event because it includes two distinct outcomes (5 and 6).
Real World Applications
Rolling a standard six-sided die and getting a prime number. The favorable outcomes are 2, 3, and 5, making it a compound event.
Drawing a face card from a standard deck of 52 playing cards, which consists of 12 different favorable outcomes (Jacks, Queens, and Kings).
Frequently Asked Questions
What is the difference between an elementary event and a compound event?
An elementary event has exactly one outcome, like rolling a 3 on a die. A compound event has more than one outcome, like rolling an odd number.
How do you find the probability of a compound event?
You calculate it by dividing the total number of favorable outcomes that make up the compound event by the total number of possible outcomes in the sample space.