Electric Motors Inc makes motors at three different factorie

Electric Motors Inc. makes motors at three different factories: Albany (A), Boston (B) and Chicago (C). Motors that come from manufacturing sometimes are Perfect (P), but sometimes they need repair (R), and other times, they are Junk (J).

The percent manufactured at each plant, and the percent of each type from each plant are in the following table:

company

%produced

%Perfect

%Repairable

%Junk

A

55

95

3

2

B

35

85

10

5

C

10

90

4

6

Calculate each of the following probabilities:

1. P(P|A)=

2. P(A|P)=

3. P(B|R)=

4. P(C|J)=

5. P(A|B)

Think about what you are given and asked. You KNOW it came from B, what is the probability it came from A?

6. P(J|R)=

Solution

1. P(P|A)=0.95

2. P(A|P)=55*0.95/(55*0.95+35*0.85+10*0.9) = 0.57412

3. P(B|R)=35*0.1/(35*0.1+55*0.03+10*0.04) = 0.6306

4. P(C|J)=10*0.06/(10*0.06 + 35*0.05+55*0.02) = 0.1739

5. P(A|B) = 0 (since A and B are mutually exclusive events).

6. P(J|R)= =