UPSC NDA Math Model Paper 9

Let E1 be th event 'Student is preparing for NDA', E2 be the event 'Student is preparing for Banking exams and X be the event 'Student was able to clear theexam'
Given: P(E1)=0.6 and P(E2)=0.4
P(X|E1)= Probability 'Student was able to clear the exam given that he/she was preparing for NDA exam' = 0.3
P(X|E2)= Probability 'Student was able to clear the exam given that he/she was preparing for Banking exams' = 0.2
Here, we have to find the value of P(E1|X).
As we know that according to bayes' theorem: P(Ei‌|‌A)=

P(Ei)‌×‌P(A‌|‌Ei)

n ∑ i‌=1 P(Ei)×P(A‌|‌Ei)

,‌ i=1,‌2,‌.......‌,‌n
⇒P(E1‌|X)=

0.6×0.3

[0.6×0.3+0.4×0.2]

=

9

13