4Quntoe 13 Check My W Exercise 4.492 Astudy of 31,000 hospital admissions i, New

Question

4Quntoe 13 Check My W Exercise 4.492 Astudy of 31,000 hospital admissions i, New York State found that 4% of the admissions led to treatmenauid and one-fourth were caused by negligence. Malpradtice re. One sever h of these treatne-aused nires rented nd payments were made in one out of every two clalims daims were iled in one out of 7.5 cases involving negligence, a admitted to the hspital will suffer a treatment-caused injury due so negligence (to 2 decimal) .01 0.004 , to 5 decimals 044673 Partlally Correet V B N M commanvd

Explanation / Answer

I have answered all questions which were showing incorrect.

a.
probability of treatment caused injuries = 0.04
probability of treatment caused by negligence = (1/4) * 0.04 = 0.01

b.
probability of treatment caused injuries resulted in death = (1/7) * 0.04 = 0.006

c.
In negligent treatment caused injury, probability of malpractice claim will be paid = (1/7.5) * (1/2) = 0.06667

Excercise 4.4
By law of total probability,
P(C) = P(C|H) P(H) + P(C|T) P(T) = 0.08 * 0.69 + 0.20 * 0.31 = 0.1172
By Bayes theorem,
P(H|C) = P(C|H) P(H) / P(C) = 0.08 * 0.69 / 0.1172 = 0.4710

C.
The probability will increase from 0.08 to 0.4710

Exercise 4.35

c.
Probability that husband as respondent thinks he is better = P(I am | Husband) =
= P(I am and Husband)/ P(Husband)
= 0.275 / 0.5 = 0.55

d.
Probability that wife as respondent thinks she is better = P(I am | Wife) =
= P(I am and Wife)/ P(Wife)
= 0.287 / 0.496 = 0.5786

e.
Given a response that "Spouse is better, the probability that response came from husband = P(Husband | My Spouse)
= P(Husband and My Spouse) / P(My Spouse) = 0.125 / 0.234 = 0.5342

f.
Given a response that "We are equal", the probability that response came from husband = P(Husband | We are equal)
= P(Husband and We are equal) / P( We are equal) = 0.1 / 0.2 = 0.5

Given a response that "We are equal", the probability that response came from wife = P(wife | We are equal)
= P(wife and We are equal) / P( We are equal) = 0.1 / 0.2 = 0.5

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