Question

1. Approximately 25% of the adult population is allergic to pets with fur or feathers, but only 4% of the adult population has a food allergy. A quarter of those with food allergies also have pet allergies.What is the probability a person has food allergies but is not allergic to pets?

A. 0.01

B. 0.03

C. 0.04

D. 0.0625

E. 0.24

2. Suppose the probability there are children in a car involved in an auto accident is 0.3. Further suppose that if there are children in a car that is involved in an auto accident, there is a 0.1 probability the driver was 55 years or older. However, if there no children in a car that is involve in an auto accident, suppose there is a 0.25 probability that driver was 55 years or older.What is the probability there were children in a car involved in an auto accident if the driver was not 55 years or older?

A. 0.66

B. 0.34

C. 0.333

D. 0.27

E. 0.01

3. Suppose the probability there are children in a car involved in an auto accident is 0.3. Further suppose that if there are children in a car that is involved in an auto accident, there is a 0.1 probability the driver was 55 years or older. However, if there no children in a car that is involve in an auto accident, suppose there is a 0.25 probability that driver was 55 years or older.What is the probability there were no children in a car involved in an auto accident if the driver was not 55 years or older?

A. 0.933

B. 0.66

C. 0.525

D. 0.34

E. 0.25

Answer 1

1) P(food allergy | pet allergy) = Quarter of pet food allergy - 1/4 x 0.04 = 0.01

P(a person has food allergies but is not allergic to pets) = P(food allergy) - P(food allergy and pet allergy)

= 0.04 - 0.01

= 0.03

2)

P(children involved | less than 55) = P(children involved and less than 55)/P(less than 55)

= 0.3x0.9/(0.3x0.9 + 0.7x0.75)

= 0.3396

3) P(no children involved | less than 55) = 1 - P(children involved | less than 55)

= 1 - 0.3396

= 0.6604