probability?

Question

PLEASE help

the probability that a person owns a cat is 89% and the probability of a person owning a sheep is 8%. the probability of someone owning both is 6%. what is the probability of someone owning neither?

Answer 1

One way to do this problem is with a Venn diagram.  Start by drawing a large rectangle and labelling it U to represent the Universal set of all people.  Draw 2 intersecting circles inside the rectangle.  Label one circle C to represent cat owners and the other circle S to represent sheep owners.  Now start filling in values for areas of regions that you know.  

 

P(owning both) = 6% so write 6% in the region where the 2 circles intersect

P(owning sheep) = 8%.  This means the entire S circle must add up to 8%.  We already have 6% in the intersecting region of the S circle so write 2% in the rest of the S circle 

P(owning cat) = 89%.  We already have 6% in the intersecting region of the C circle so write 83% in the rest of the C circle 

 

The numbers you have written down add up to 83 + 6 + 2 = 91%.  So the remaining 9% of the people must be in the region outside the 2 circles but still within the rectangle.  These are the people who own neither a cat nor a sheep, so P(own neither) = 9%  

 

There are other ways to do this problem using probability formulas, but I think the Venn diagram approach is the most instructive for beginners.