In the movie A Christmas Story, Ralph wanted an official Red Ryder carbine actio
ID: 3206551 • Letter: I
Question
In the movie A Christmas Story, Ralph wanted an official Red Ryder carbine action 200 shot rang model BB gun. EVeryone in the movie tells Ralphie he will shoot his eye out with his present. According to the Centers for Disease Control and Prevention, approximately 30,000 people visted an Emergancy Room last year for BB gun accidents. The most common injuries were to the face, head, neck, and eye. In a survey for BB and pellet gun related injuries treated at hospitals each injury was classified by primary body part injured and victim-shooter relationship. The results are given below:
EYE
OTHER
23
2
20
3
9
3
3
2
7
1
26
5
Suppose this table is representative of the entire population of BB gun injuries, and a person seen in an Emergency Room suffering from this type of injury is selected at random.
a.) What is the probabililty that the injury is to the eye and that the shooter is a relative?
b.) Suppose the injury was caused by a stranger. What is the probabillity that the body part injured is an extremity?
c.) Suppose the injuy is to the head/neck. What is the probability that the shooter is a friend/acquaintance?
d.) Suppose the injury is not to the eye. What is the probability that the shooter is a relative?
SELF FRIEND/ACQUAINTANCE RELATIVE STRANGER OTHER/SHOOTER NOT SEEN NOT STATED EXTREMITY 200 128 89 17 25 189 TRUNK 57 40 21 5 10 58 FACE 51 35 20 4 14 49 HEAD/NECK 40 34 19 6 12 44EYE
OTHER
23
2
20
3
9
3
3
2
7
1
26
5
Explanation / Answer
a.) What is the probabililty that the injury is to the eye and that the shooter is a relative?
Probabililty that the injury is to the eye and that the shooter is a relative
= Value at Row: Eye Column:Relative/Grand Total = 9/1271 = 0.007081
b.) Suppose the injury was caused by a stranger. What is the probabillity that the body part injured is an extremity?
Probabillity that the body part injured is an extremity given the injury was caused by a stranger
= Value at row:extremity column:stranger / Column total stranger = 17/37 = 0.459459
c.) Suppose the injuy is to the head/neck. What is the probability that the shooter is a friend/acquaintance?
Probability that the shooter is a friend/acquaintance given the injury is to the head/neck
= Value at column : Friend/acquaintance row :head/neck / row total Head/neck = 34/155 = 0.219355
d.) Suppose the injury is not to the eye. What is the probability that the shooter is a relative?
Probability that the shooter is a relative given that the injury not to the eye =
(Column Total under Relative - value at row:eye Column : relative) / (Grand total - Row total under Eye)
= (161 - 9) / (1271-88) = 152/1183 = 0.128487
SELF FRIEND/ACQUAINTANCE RELATIVE STRANGER OTHER/SHOOTER NOT SEEN NOT STATED Total EXTREMITY 200 128 89 17 25 189 648 TRUNK 57 40 21 5 10 58 191 FACE 51 35 20 4 14 49 173 HEAD/NECK 40 34 19 6 12 44 155 EYE 23 20 9 3 7 26 88 Other 2 3 3 2 1 5 16 Total 373 260 161 37 69 371 1271Related Questions
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