Question

In: Statistics and Probability

2. Define and show using Venn diagrams, the following: 2.1 The union of two events. 2.2...

2. Define and show using Venn diagrams, the following:

2.1 The union of two events.

2.2 The intersection of two events.

2.3 The complement of an event in a sample space.

3. Write some limitations of Venn diagrams as discussed in the class.

Expert Solution

2. Define and show using Venn diagrams, the following:

2.1 The union of two events.

2.2 The intersection of two events.

2.3 The complement of an event in a sample space.

3. Write some limitations of Venn diagrams as discussed in the class.

Soln

2.1)

The union of two Events is given by the shaded region in the below diagram.

Union means: the new set that contains every element from either of A and B

2.2)

The intersection of two Events is given by the shaded region in the below diagram.

Intersection means the new set that contains every element that is in both of the input sets; only things inside both input sets get added to the new set

2.3)

The intersection of an event (A) is given by the shaded region in the below diagram.

Compliment: the new set gets everything that is in the universe but is outside of A; it's okay if the element is in B, just so long as it is not also in A

3)

Limitation of Venn Diagram is that when we have more than 4 sets, visualization becomes difficult. Also, solving for more than 4 sets becomes very difficult.

orchestra answered 2 years ago

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