In 1986 puiblished study about the treatments of kidney stones two diffe- rent t
ID: 3365768 • Letter: I
Question
In 1986 puiblished study about the treatments of kidney stones two diffe- rent therapies have been made on 350 patients. The success oft he therapy depended on the size oft the stone. The absolute numbers oft he success- ful treatments are in the following table: Therapy A Therapy B absolute percentua absolute percentual Small stones 81 of 87 Big stones 192 of 263 total 234 of 270 55 of 80 289 of 350 297 of 350 1) Calculate the percentual portion oft he successful therapy. Which see- mingly contradiction do you see between the success of therapy a and therapy b? 2) Explain with conditional probability, this contradiction.Explanation / Answer
Therapy A
Therapy B
Absolute
Percentual
Absolute
Percentual
Small Stones
81/87
93.10
234/270
86.67
Big Stones
192/263
73.00
55/80
68.75
Total
273/350
78.00
289/350
82.57
Here the contradiction arises since the therapy A has more chances to cure individual cases i.e. of the small stones and big stones cases separately but therapy B has more chances of success when compared with total number of cases.
Let
A is the event of selection of therapy A
B is the event of selection of therapy B
S denotes the success of small stone cases
L denotes the succes of big stone cases
T denotes the event of total success of cases
So here
P[S|A]=0.9310 > P[S|B]=0.8667
P[L|A]=0.73 > P[L|B]=0.6875
BUT
P[T|A]=0.78 < P[T|B]=0.8257
Therapy A
Therapy B
Absolute
Percentual
Absolute
Percentual
Small Stones
81/87
93.10
234/270
86.67
Big Stones
192/263
73.00
55/80
68.75
Total
273/350
78.00
289/350
82.57