Probability: Conditional In-Depth (Dependent Events)
In the Probability Rules and Terms page, we introduced the concept of dependent events. The definition is below:
One way to help identify whether or not the problem deals with dependent events is to look for the key word "given." The probability of A given B is dependent because the occurrence of B affects the probability of A occurring. A real-life example of this would be: "What is the probability that team A wins given that they are leading by 20 points?"
The probability of event A occurring given that event B has already occurred is written with the notation P(A | B) and read as "the probability of A given B."
A random person's survey results were viewed. What is the probability that this individual chose a dog as their favorite pet given that they chose baseball as their favorite sport?
|Solution A (Using Mathematics)||Solution B (Using Logic)|
|Through inspection, we know that there are own only 47 individuals who like baseball. If we took those 47 into a separate room, then randomly picked a person, what would be the probability that this person liked dogs the most? Well of the 47 individuals, 10 like dogs. Thus, the probability a person likes a dog the most, given that they like baseball the most, is simply 10/47 or 0.213.|
Multiplication Rule for Related Events
If two events, A and B, are NOT independent events, then the probability of A and B is equal to the probability of A times the probability of B given A.
Tree Diagrams are a powerful tool for conditional probability. To see examples of problems being solved with this tool, click on the Tree Diagram help page.