Answer to Question #223385 in Statistics and Probability for ilo

Question

. Thirty-six percent of all U. S. households have a pet dog. Thirty-four percent of all U. S. households have a pet cat. Two percent of all U. S. households have a horse and interestingly, eighty percent of households with a horse, also own a dog. (Of course, households with a horse and a dog would also be part of the 36% with a dog.) A U. S. household is chosen at random.

(a)  What is the probability it has a dog?

 

(b)  What is the probability it has a dog or a cat?

 

(c)  What is the probability it has a horse?

 

(d)  What is the probability it has a dog and a horse?

 

(e)  What is the probability it has a horse only?

 

(f)   What is the probability it has a dog only?

 

Answer 1

Let use the sample of 1000 U.S. households.

Number of households that have a pet dog $= 1000 \times 0.36 = 360$

Number of households that have a pet cat $= 1000 \times 0.34 = 340$

Number of households that have a horse $= 1000 \times 0.02=20$

Number of households with a horse, also own a dog $= 20 \times 0.8 = 16$

(a) P(has a dog) $= \frac{360}{1000}= 0.36$

(b) P(has a dog or a cat) $= \frac{360+340}{1000}= 0.7$

(c) P(has a horse) $= \frac{20}{1000}= 0.02$

(d) P(has a dog and a horse) $= \frac{16}{1000}=0.016$

(e) P(has a horse only) $= \frac{20-16}{1000} = 0.004$

(f) P(has a dog only) $= \frac{360-16}{1000}=0.344$