the chance that doctor will diagnose a disease is 70% the chance os of death of patient after correct diagnose is 35% while after wrong diagnose is 80% find probablity of duagnosed cirrectly or wrong
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>>Bayes Theorem
>>The chance that Doctor A will diagonise
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The chance that Doctor A will diagonise disease X correctly is 60%. The chance that a patient will die by his treatment after correct diagnosis is 40% and the chance of death after wrong diagnosis is 70%. A patient of Doctor A who had disease X died. The probability that his disease was diagonised correctly is
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Correct option is B)
Let us define the following events.
E
1
: Disease X is diagnosed correctly by doctor A.
E
2
: Disease X is not diagnosed correctly by doctor A.
B: A patient (of doctor A) who has disease X dies.
Then, we are given, P(E
1
)=0.6,P(E
2
)=1−P(E
1
)=1−0.6=0.4
and P(
E
1
B
)=0.4, P(
E
2
B
)=0.7
By Bay's Theorem
P(
B
E
1
)=
P(E
1
)P(
E
1
B
)+P(E
2
)P(
E
2
B
)
P(E
1
)P(
E
1
B
)
=P(
B
E
1
)=
0.6×0.4+0.4×0.7
0.6×0.4
=
0.24+0.28
0.24
=
0.52
0.24
=
13
6