UPSC NDA Math Model Paper 7

Let E1,E2 and E3 be the events that boxes A,B and C are chosen respectively.
⇒P(E1)=P(E2)=P(E3)=1∕3
Let X be the event that the gold coin drawn is gold.
⇒P(X|E1)=P( A gold coin is drawn from bag A)=2∕2=1
⇒P(X|E2)=P( A gold coin is drawn from bag B)=0
⇒P(X|E3)=P( A gold coin is drawn from bag C)=1∕2
Now the probability that the other coin in the box is gold = The probability that gold coin is drawn from box A = 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)=

1 3 .1

[ 1 3 .1+ 1 3 .0+ 1 3 . 1 2 ]

=

2

3