3. Two bags A and B contain 4 white, 3 black balls and 2 white and 2 black balls respectively. From
bag A, two balls are transferred to bag B. Find the probability of drawing2 white ball from bag b
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Answer:
Let us consider the problem,
S
i
be the event that you selected bag i; W,B that you selected a white or black ball.
So, 'randomly selected' we selecting either bag is equally likely.
P(S
A
∣B)=
P(B)
P(S
A
,B)
=
P(S
A
,B)+P(S
B
,B)
P(B∣S
A
)P(S
A
)
=
P(B∣S
A
)P(S
A
)+P(B∣S
B
)P(S
B
)
P(B∣S
A
)P(S
A
)
=
(
5
3
)(
2
1
)+(
12
7
)(
2
1
)
(
5
3
)(
2
1
)
=
71 /36
Hence, the probability of white ball is
71 /36
Step-by-step explanation:
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