A study of 31,000 hospital admissions in New York State found that 4% of the adm
ID: 2956959 • Letter: A
Question
A study of 31,000 hospital admissions in New York State found that 4% of the admissions led to treatment-caused injuries. One-seventh of these treatment-caused injuries resulted in death, and one-fourth were caused by negligence. Malpractice claims were filed in one out of 7.5 cases involving negligence, and payments were made in one out of every two claims.a. What is the probability a person admitted to the hospital will suffer a treatment-caused injury due to negligence? (4%)
b. What is the probability a person admitted to the hospital will die from a treatment-caused injury? (4%)
c. In the case of a negligent treatment-caused injury, what is the probability a malpractice claim will be paid? (4%)
Explanation / Answer
SIMPLE ARITHMETIC:a. What is the probability a person admitted to the hospital will suffer a treatment-caused injury due to negligence?
4% of 31000 suffer a treatment-caused injury.
and one-fourth were caused by negligence.
1/4 of 4% is 1% or a probability 0:
Probability of having a treatment related injury P(injury) is 4% or 0.04
Among these probability that is is due to negligence P(negligence) is 1/4 or 0.25
Probability of (injury due to negligence) = P(injury) . P(negligence) = 0.25 x 0.04 = 0.01
b. What is the probability a person admitted to the hospital will die from a treatment-caused injury? (4%)
Similar logic:
Probability of having a treatment related injury P(injury) is 4% or 0.04
Among these probability that is results in death P(death) is 1/7
Probability of (injury resulting in death) = P(injury) . P(death) = 1/7 x 0.04 = 1/175 or 0.0057143..
c. In the case of a negligent treatment-caused injury, what is the probability a malpractice claim will be paid? (4%)
Similar logic but read the question well. It does not ak the probability in the general admission case like probability of paid claim WHEN there is an injury. So the 4% is taken as having already happened. It is not conditional, it is fact.
Probability of having a treatment related injury P(injury) is irrelevant
Among these probability of malpractice claim P(claim) is 1/7.5
Among these of paid claim P(payment) is 1/2
Probability of (paid claim when injury) =
P(claim) . P(payment) = 1/2 x 1/7.5 = 1/15 or 0.06666666..
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