I want to discuss the meaning of the complement of an event

I want to discuss the meaning of the complement of an event, addition law and mutually exclusive events. You will need to understand their meaning before answering the questions. How do we use each in the determination of probabilities for an event?

Also, how does conditional probability and independent affect how we look at a population?

Solution

Complement of a event:- Let us denote an event A and the sample space is S. The complement of the event A is the set of all the outcomes in the sample space S that are not included in the outcomes of event A. It is denoted by A\'. P (A\') = 1 - P (A).

Addition Law:- Let A and B are 2 events. According to the addition law, the probability of A or B is given as

Mutually Exclusive Events:- When 2 events A and B are mutually exclusive, they cannot occur together, i.e., their intersection is a null event. P (A and B) = 0.

When the affect are independent, then the conditional probability is same as the unconditional one. Let A and B be 2 independent events. Then, P (B|A) = P (B).