Question

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?

The Centers for Disease Control and Prevention estimate that approximately 100,000 Americans suffer nonfatal dog- and cat-associated falls each year. 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 P, and P2", where P, and P2 are the two probabilities.) Age of Injured Individual (years) 15-34 35-54 55-74 75 or over 14 or under Dog 0.15 0.16 0.19 0.12 Pet Involved in Injury Cat 0.01 0.04 0.02 0.02

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?

Answer 1

Let p1 be the probability that a man or lady in age group 35-54 injured by a dog

p2 be the probability that a man or lady in age group 15-34 injured by a cat

then 0.15+0.16+p1+0.19+0.12+0.01+p2+0.04+0.02+0.02=1

hence p1+p2=1-0.71=0.29

p1=0.29-p2.hence the value of p1 and p2 lies in the interval$\sqsubset 0,0.29\sqsupset$

a) 0.12

b)let A be the event that injured person is between 55 and 74 years old.B1 be the event of injury by dog and B2 be the event of injury by cat

then P(A)= P(A/B1)*P(B1)+P(A/B2)*P(B2)

=0.19*(0.62+p1) +0.02*(0.09+p2)

=0.1196+0.19p1+0.02p2

hence P(A) lies in the interval $\sqsubset 0.1254,0.1747\sqsupset$ as value of p1 and p2 lies in the interval$\sqsubset 0,0.29\sqsupset$

c) Atleast 55 include the age group 55-74 and 75 or over and let this event be B

p(Atleast 55)= P(B)=P(B/B1)*P(B1)+P(B/B2)*P(B2)

=0.31*(0.62+p1) +0.04*(0.09+p2)

=0.1958+0.31p1+0.04p2.

hence P(A) lies in the interval$\sqsubset 0.199396,0.2857\sqsupset$ as value of p1 and p2 lies in the interval$\sqsubset 0,0.29\sqsupset$

d) 0.02+0.15=0.17