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.

What is the probability a person admitted to the hospital will suffer a treatment-caused injury due to negligence (to 2 decimals)?

b. What is the probability a person admitted to the hospital will die from a treatment caused injury (to 3 decimals)?

c. In the case of a negligent treatment-caused injury, what is the probability a malpractice claim will be paid(to 5 decimals)?

Answer 1

SOLUTION:-

Given that the study of 31,000 hospital admissions that contains 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) Now, we have to find the probability that a person admitted to the hospital will die from a
treatment-injury due to negligence

P(injury) = 4% = 0.04

P(neghgence) = Z = 0.25

The required probability is, Probability of (injury due to negligence)

P(injury)x P(negligence)

0.25 x 0.04

b) Now, we have to find the probability that a person admitted to the hospital will die from a
treatment caused injury
P(injury) = 4% = 0.04 P(death) =1/7
The required probability is. Probability Of (injury resulting in death) = P(injury)x P(death)
l/7 x 0.04

0.0057!

c) Now, we have to find the probability of having a treatment related injury is irrelevant
Probability of malpractice claim P(claim) =1/ 7.5 Probability of payment is, P(paymem)=1/2
The required probability is, Probability of (paid claim when injury)
P(claim)x P(payment)
l/2x1/7.5
=
0.0667