Information Technology Reference
In-Depth Information
Solution
P
1
)=2000/6000=1/3
(3) If that the product comes from
(
A
1
·
B
A
1
is known, how much is the probability that
it belongs to
B
1
?
Solution
P
1
)=2000/3000=2/3
(4) If the product belongs to
(
B
1
|
A
B
2
, how much is the probability that it comes from
A
3
respectively?
Solution
P
1
,
A
2
, or
A
(
A
1
|
B
2
)=1000/2000=1/2
P
(
A
|B
2
)=500/2000=1/4
2
2
)=500/2000=1/4
2. Calculate the following probabilities with Conditional Probability
(1) If a product comes from
P
(
A
3
|
B
A
1
, how much is the probability that it belongs to
B
1
?
Solution:
P
B
1
|
A
1
)=(1/3)/(1/2)=2/3
(2) If a product belongs to
B
2
, how much is the probability that it comes from
(
A
1
,
A
2
, or
A
3
respectively?
Solution
:
P
(
A
1
|
B
2
)=(1/6)/(1/3)=1/2
P
(
A
2
|
B
2
)=(1/12)/(1/3)=1/4
B
2
)=(1/12)/(1/3)=1/4
3. Calculate the following probabilities with Bayesian Formula
.
P
(
A
3
|
(1) Known:
P
(
B
1
)=4000/6000=2/3
P
(
B
2
)=2000/6000=1/3
P
(
A
1
|
B
1
)=1/2
2
)=1/2
Question: If a product comes from
P
(
A
1
|
B
A
1
, how much is the probability that it belongs
to
2
?
Solution:
Calculate Joint Probabilities:
B
P
(
B
1
)
P
(
A
1
|
B
1
)=(2/3)(1/2)=1/3
2
)=(1/3)(1/2)=1/6
Calculate Total Probability:
P
(
B
2
)
P
(
A
1
|
B
1
)=(1/3)+(1/6)=1/2
Calculate posterior probability according to Bayesian Formula:
P
(
A
P
(
B
2
|
A
1
) = (1/6) ÷ (1/2) = 1/3
(2) Known:
P
(
A
1
)=3000/6 000=1/2
P
(
A
2
)=2000/6 000=1/3
P
(
A
3
)=1000/6 000=1/6
P
(
B
2
|
A
1
)=1000/3 000=1/3
