Test Index

NCERT Class XII Mathematics Chapter - - Solutions

© examsnet.com
Question : 37
Total: 101
A bag contains 4 red and 4 black balls, another bag contains 2 red and 6 black balls. One of the two bags is selected at random and a ball is drawn from the bag which is found to be red. Find the probability that the ball is drawn from the first bag.
Solution:  
Let E1  : ‘first bag is selected’, E2 : ‘second bag is selected’ and
A : ‘Red ball is drawn’ Also, P(E1)=P(E2)=
1
2

P (red ball is drawn when first bag is selected) =P(A|E1)=
4
8

P(red ball is drawn when second bag is selected) =P(A|E2)=
2
8

Hence the required probability
P(E1|A) =
P(A|E1)P(E1)
P(A|E1)P(E1)+P(A|E2)P(E2)

=
4
8
×
1
2
(
4
8
×
1
2
)+(
2
8
×
1
2
)
=
2
3
© examsnet.com
Go to Question:
Prev Question
Next Question