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NCERT Class XII Mathematics Chapter - - Solutions

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Question : 95
Total: 101
Assume that the chances of a patient having a heart attack is 40%. It is also assumed that a meditation and yoga course reduce the risk of heart attack by 30% and prescription of certain drug reduces its chances by 25%. At a time a patient can choose any one of the two options with equal probabilities. It is given that after going through one of the two options the patient selected at random suffers a heart attack. Find the probability that the patient followed a course of meditation and yoga ?
Solution:  
E1 : Patient follows meditation and Yoga
E2 : Patient uses drug and A : Patient suffers a heart attack.
∴P(E1)=P(E2)=
1
2
, P(A)=40%=0.4
Also P(A|E1)=
40
100
(1−
30
100
)=
28
100

(∵ Yoga & meditation reduces heart attack by 30%)
and P(A|E2)=
40
100
(1−
25
100
)=
30
100

(∵ drug prescription reduces heart attack by 25%)
By Bayes’ theorem,
P(E1|A)=
P(E1).P(A|E1)
P(E1).P(A|E1)+P(E2).P(A|E2)
=
(
1
2
)(
28
100
)
1
2
×
28
100
+
1
2
×
30
100
=
14
29
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