Unions and Intersections in Mathematics! Applications to insurance!

Hello All!

This is an Algebra lesson, but it can be applied to Statistics in a big way! So, though I would give you an old math lesson everyone should understand. I will explain more on how you can use this in Statistics as well!

Notation

• P() means the probability of
• A and B are events that happen
• ∩-intersection
• ∪-union

Example

An insurance company has car and motorcycle insurance. 85% of customers have car insurance and 3% of customers have both car and motorcycle insurance. How many people have motorcycle insurance?
It's best to draw a venn diagram for explaining these types of problems, but there is an equation for it...

P(A∪B)=P(A)+P(B)-P(A∩B) (All this says is that the probability of A or B happening is equal to the probability of A plus the probability of B minus the probability of both happening)

Here is our 1st venn diagram:

Here is our solution venn diagram after some thought and work:

Again, the mathematical equation works if you can read it. We see that the answer is 18%.

It is a good common problem to know! Let me know if you have questions. Thank you for your support Steemers! Enjoy learning and teach your kids.