# 1. How can we analyse events using the union and intersection of sets? 2. Explain the implications of dependent and independent event?

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### 1 Answer

In mathematics, the term event refers to a set of possible outcomes when certain conditions are met. For example, the event of getting an even number when a die is rolled is given by the set {2,4,6}. This is a subset of the sample space {1,2,3,4,5,6} which has all the numbers that one can get when a die is rolled.

Let set {A} and set {B} represent two events. The union of the two sets represents a set of outcomes when either the conditions that satisfy event A or the conditions that satisfy event B or the conditions that satisfy both A and B are met. The union of the two sets represents a set of outcomes when both the conditions that satisfy event A and those that satisfy event B are met. To illustrate this let event A occur when a number chosen from the sample space {1,2,3,4,5,6,7,8,9,10} is even. {A} is {2,4,6,8,10}. Let event B occur when a number chosen from the sample space is greater than 3. {B} is {4,5,6,7,8,9,10}. The union of the two sets is {2,4,5,6,7,8,9,10} and is the event of choosing a number from the sample space that is either even or greater than 3. The intersection of the two sets is {4,6,8,10} and is the event of choosing a number from the sample space that is both even as well as greater than 3.

Two events are independent when the outcome of either of the events is not dependent on the outcome of the other event. If the outcome of either of the events is dependent on the outcome of the other event, they are said to be dependent.

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