Find the probability that it was drawn from Bag II Solution Let E1 be the event of choosing the bag I, E2 the event of choosing the bag II
and A be the event of drawing a red ball Then
P(E1) = P(E2) =  1
2
Also
P(A|E1) = P(drawing a red ball from Bag I) = 3
7
and
P(A|E2) = P(drawing a red ball from Bag II) = 5
11
Now, the probability of drawing a ball from Bag II, being given that it is red,
is P(E2|A)
By using Bayes' theorem, we have
P(E2|A) =
2
2
1
1
2
2
P(E )P(A|E )
P(E )P(A|E )+P(E )P(A|E )  = 
1
5
35
2 11
1
3
1
5
68
2
7
2 11
×
=
×
+
×
Example 17 Given three identical boxes I, II and III, each containing two coins In
box I, both coins are gold coins, in box II, both are silver coins and in the box III, there
is one gold and one silver coin