Probability Rules
Overview:
The following are a list of rules you may use when dealing with different probability. These are used when trying to find the chance that an event or events may occur.
Addition Rule
For two disjoint events A and B, the probability that one or the other occurs is the sum of the probabilities of two events. Disjoint events have no outcomes in common.
General Addition Rule
There are times when you’re going to run into probabilities that are not disjoint and share a common outcome. If that does not happen you will be using this rule.
By doing this rule you’ll be adding the probability of the two events and then subtracting out the common areas/ intersections.
Multiplication Rule
When solving the probability of two independent events A and B, the probability that both A and B will occur is the product of the probabilities of the two events.
General Multiplication Rule
This rule is used for compound events that do not necessarily have to be independent.
Complement Rule
The probability of an event occurring is 1 minus the probability it doesn’t occur. The set of outcomes that are not in the event A is called the complement of A and is denoted Ac.
Good Rules of Thumb:
Though solving probability problems might be troublesome by looking out for certain words you’ll know what to do
Example 1:
Lewis is to choose one ball from a sack. The sack contains six red balls, four green balls, two yellow balls, and three purple balls. What is the probability of Lewis getting a green or yellow ball?
Solution:
4/15: number of green balls/total balls
2/15: number of yellow balls/total balls
4/15 + 2/15 = 6/ 15 = 2/ 5 = 40%
Example 2:
A survey of college students found that 64% live in a campus residence hall, 72% have a car, and 45% live on campus and have a car. What’s the probability that a randomly selected student lives on campus or has a car?
Solution:
64% -> .64: percentage of student living in a campus residence hall
72% -> .72: percentage of students who own a car
45% -> .45: percentage of students who live on campus and have a car
.64 + .72 - .45 = .91
The following are a list of rules you may use when dealing with different probability. These are used when trying to find the chance that an event or events may occur.
Addition Rule
For two disjoint events A and B, the probability that one or the other occurs is the sum of the probabilities of two events. Disjoint events have no outcomes in common.
- P(A B) = P(A) + P(B)
General Addition Rule
There are times when you’re going to run into probabilities that are not disjoint and share a common outcome. If that does not happen you will be using this rule.
- P(A B) = P(A) + P(B) – P(AB)
By doing this rule you’ll be adding the probability of the two events and then subtracting out the common areas/ intersections.
Multiplication Rule
When solving the probability of two independent events A and B, the probability that both A and B will occur is the product of the probabilities of the two events.
- P (AB) = P(A) x P(B)
General Multiplication Rule
This rule is used for compound events that do not necessarily have to be independent.
- P (AB) = P(A) x P(B | A)
Complement Rule
The probability of an event occurring is 1 minus the probability it doesn’t occur. The set of outcomes that are not in the event A is called the complement of A and is denoted Ac.
- P(A) = 1 – P(Ac)
Good Rules of Thumb:
Though solving probability problems might be troublesome by looking out for certain words you’ll know what to do
- Not - subtract from 1
- At least- subtract from 1
- Or- add (must be disjoint)
- And- multiply (must be independent)
Example 1:
Lewis is to choose one ball from a sack. The sack contains six red balls, four green balls, two yellow balls, and three purple balls. What is the probability of Lewis getting a green or yellow ball?
Solution:
4/15: number of green balls/total balls
2/15: number of yellow balls/total balls
4/15 + 2/15 = 6/ 15 = 2/ 5 = 40%
Example 2:
A survey of college students found that 64% live in a campus residence hall, 72% have a car, and 45% live on campus and have a car. What’s the probability that a randomly selected student lives on campus or has a car?
Solution:
64% -> .64: percentage of student living in a campus residence hall
72% -> .72: percentage of students who own a car
45% -> .45: percentage of students who live on campus and have a car
.64 + .72 - .45 = .91