I need help with these probability questions for geometry

Question

Customers entering Petsmart were surveyed at random about what type of pet they had. The results showed that the probabitlity of a person owning a dog was .56. The probabilty that a person had both a dog and a cat was .20 and the probability that the customer had neither a dog nor a cat was .12.

If D represents customers who own a dog and C represents customers who own a cat. What notation represents the customers that own only a cat?

Find the following probablities from the above problem.  Round to the nearest hundredth.

a) P(C or D)  

b) P(C and D)   

c) P(Not D)     

d) P(D only)  

e) P( D | C)  

 

Answer 1

a) P(C or D)  = 1 - P(not (C or D) = 1 - 0.12 = 0.88 

b) P(C and D)   = 0.2 (given)

c) P(Not D)     = 1 - P(D) = 1 - 0.56 = 0.44

d) P(D only)  = P(D) - P(C and D) = 0.56 - 0.2 = 0.36

e) P(C) = 1 - P(D) only - P(not (C or D) = 1 - 0.36 - 0.12 = 0.52

P( D | C)  = P(D and C)/P(C) = 0.2/0.52 = 0.38

Answer 2

Imagine a Venn Diagram with 2 overlapping circles.

Circle D will represent people with dogs and circle C will represent people with cats.

The overlap is people with both dogs and cats and that is .20, therefore the probability of a dog only is .56 - .20 = .36.

Now subtract .36 and .20 and .12 from 1.00 and you get the probability of a customer having a cat only which will be .32.

Now add .32 and .20 and that would be having a cat with or without a dog which is .52.

Now we can answer each question.

a) That would be .36 + .20 + .32 = .88 or 1.00 - .12 = .88

b)That is .20 which is given

c) That would be 1.00 - .56 = .44

d) .36 as calculated above

e) This means what is the probability of having a dog given that one already has a cat.

So that would be .20/.52 = .38 rounded