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Addition Rule for Probabilities

Addition Rule for Probabilities can be defined as the statistical property that states the probability of one and/or two events. These events occurring at the same time is equal to the probability of the first event occurring plus the probability of the second event occurring as well as to minus the probability that both events occur at the same time. 

The addition rule helps to solve the probability problems that involve two events and suppose the two events that are usually labeled as A and B and the events are performing any one of the tasks such as rolling dice and drawing cards as well as spinning a spinner and finding about the probability of two things happening in that one task. When it is required to find the probability of A or B it is meant that either A can happen or B can happen as well as both can happen together that is what is stated in the addition rule. 

The rule of addition usually applies to the following situation such that. We have two events, and we want to know the probability that either event occurs.

Addition Rule of Probabilities Assignment Help

Rule of Addition can be defined as the probability that Event A can occur or Event B can occur is equal to the probability that Event A occurs plus the probability that Event B occurs minus the probability that both Events A and B occur and this can be represented as follows:

P(A ∪ B) = P(A) + P(B) - P(A ∩ B))

Invoking the fact that P(A ∩ B) = P( A )P( B | A )

,

The addition rule can also be expressed as

P(A ∪ B) = P(A) + P(B) - P(A)P( B | A )

 

Addition Rule of Probabilities Homework Help

Example: Suppose a student goes to the library and the probability that she checks out for a work of fiction is 0.40 and the probability that she looks for work of non-fiction is 0.30 , and the probability for both fiction and non-fiction is 0.20 , then find out the probability that the student checks out a work of fiction and non-fiction as well as for both?

 

Solution: Let F is the event that the student checks out fiction. Let N is the event that the student checks out non-fiction is

P(F ∪ N) = P(F) + P(N) - P(F ∩ N)

P(F ∪ N) = 0.40 + 0.30 - 0.20 = 0.50

 

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