The Centers for Disease Control and Prevention estimate that approximately 100,0
ID: 3356999 • Letter: T
Question
The Centers for Disease Control and Prevention estimate that approximately 100,000 Americans suffer nonfatal dog- and cat-associated falls each year.1 The table below, which was unfortunately damaged by some spilled coffee, shows how these injuries are distributed over age groups and pet associated with the injury. For example, 15% of these injuries are dog-associated injuries in children who are 14 years old or less. Prior to the damage to the table, the values represented a legitimate probability model—the 10 cells are mutually exclusive and exhaustive, each entry in the table was between 0 and 1, and the 10 values added up to 1. If, due to the damage to the table, you are unable to provide an exact answer to a question, you should provide the narrowest range within which the answer must fall. (For example, say “Between P1 and P2”, where P1 and P2 are the two probabilities.)
a) Suppose one injured individual is selected at random. What is the probability that this person is 75-or-over and experienced a dog-related injury?
b) Suppose one injured individual is selected at random. What is the probability that this person is between 55 and 74 years old?
c) Suppose one injured individual is selected at random. What is the probability that this individual is at least 55 years old (i.e., is 55 years old or older)?
d) Suppose one injured person is selected at random. What is the probability that he or she is 75-or-over with a cat-related injury OR 14-or-under with a dog-related injury?
e) Suppose one injured individual is selected at random. What is the probability that he or she is between 15 and 54 years old?
f) Suppose one individual is selected at random. What is the probability that he or she experienced a cat-related injury?
Age in years age in years age in years age in years age in years 14 or under 15-34 35-54 55-74 75 or over DOG 0.15 0.16 0.19 0.12 CAT 0.01 0.04 0.02 0.02Explanation / Answer
a) probability that this person is 75-or-over and experienced a dog-related injury =0.12
b) probability that this person is between 55 and 74 years old =0.19+0.02 =0.21
c) probability that this individual is at least 55 years old =0.19+0.02+0.12+0.02=0.35
d) probability that he or she is 75-or-over with a cat-related injury OR 14-or-under with a dog-related injury
=0.02+0.15 =0.17
e)
probability that he or she is between 15 and 54 years old =1-(0.15+0.01+0.19+0.02+0.12+0.02)=0.49
f)probability that he or she experienced a cat-related injury =between 0.09 to 0.38
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