Respuesta :
Answer:
(a) The probability a person admitted to the hospital will suffer a treatment-caused injury due to negligence is 0.01.
(b) The probability a person admitted to the hospital will die from a treatment caused injury is 0.006.
(c) In the case of a negligent treatment-caused injury the probability a malpractice claim will be paid is 0.06667.
Step-by-step explanation:
Denote the events as follows:
X = treatment-caused injuries
A = injuries resulted in death
B = injuries were caused by negligence
C = Malpractice claims were filed
D = payments were made in cases where claims were filed.
The information provided is:
[tex]P(X)=0.04\\P(A|X)=\frac{1}{7}\\P(B|X)=\frac{1}{4}\\P(C|B)=\frac{1}{7.5}\\P(D|C)=\frac{1}{2}[/tex]
The multiplication rule of probability is:
[tex]P(U\cap V)=P(U|V)\times P(V)=P(V|U)\times P(U)[/tex]
(a)
Compute the value of P (X ∩ B) as follows:
[tex]P(X\cap B)=P(B|X)P(X)=\frac{1}{4}\times 0.04=0.01[/tex]
Thus, the probability a person admitted to the hospital will suffer a treatment-caused injury due to negligence is 0.01.
(b)
Compute the value of P (X ∩ A) as follows:
[tex]P(X\cap A)=P(A|X)P(X)=\frac{1}{7}\times 0.04=0.0057\approx0.006[/tex]
Thus, the probability a person admitted to the hospital will die from a treatment caused injury is 0.006.
(c)
Compute the value of P (C ∩ D | B) as follows:
[tex]P(C\cap D|B)=P(C|B)\times P(D|C)=\frac{1}{7.5}\times \frac{1}{2}=0.06667[/tex]
Thus, in the case of a negligent treatment-caused injury the probability a malpractice claim will be paid is 0.06667.
