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Standard XII
Mathematics
Conditional Probability
A bag contain...
Question
A bag contains 4 white balls and 2 black balls. Another contains 3 white balls and 5 black balls. If one ball is drawn from each bag, find the probability that
(i) both are white
(ii) both are black
(iii) one is white and one is black
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Solution
Given:
Bag 1=
4W+2B
balls
Bag 2=
3W+5B
balls
i
P
both are white
=
4
6
×
3
8
=
1
4
ii
P
both are black
=
2
6
×
5
8
=
5
24
iii
P
one is white and one is black
=
P
white from bag 1 and black from bag 2
+
P
white from bag 2 and black from bag 1
=
4
6
×
5
8
+
3
8
×
2
6
=
20
48
+
6
48
=
26
48
=
13
24
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