Consider again Figure 125 and the two assembly lines Calcula

Consider again Figure 1.25 and the two assembly lines. Calculate the probabilities: (a) Both lines are at full capacity conditional on neither line being shut down (b) At least one line is at full capacity conditional on neither line being shut down (c) One line is at full capacity conditional on exactly one line being shut down (d) Neither line is at full capacity conditional on at least one line operating at partial capacity

Solution

. A factory has two assembly lines, each of which is shutdown (S), at partial capacity (P), or at full capacity (F).The probability values for the assembly line operations are shown below.


Assembly Line/
Operation
2- Shutdown
2- Partial Capacity
2- Full Capacity
1- Shutdown 0.02 0.06 0.05
1-Partial Capacity 0.07 0.14 0.20
1- Full Capacity 0.06 0.21 0.19

For example, the probability that the first assembly line is shut down and the second one is operating at partial capacity is 0.06.

What is the probability that:

A. both assembly lines are shut down?
B. neither assembly line is shut down?
C. at least one assembly line is at full capacity?
D. exactly one assembly line is at full capacity?
E. both lines are at full capacity conditional on neitherline being shut down?
F. at least one line is at full capacity conditional onneither line being shut down?
G. one line is at full capacity conditional on exactly oneline being shut down?
H. neither line is at full capacity conditional on at leastone line operating at partial capacity?

Answer

A factory has two assembly lines, each of which is shutdown (S), at partial capacity (P), or at full capacity (F).The probability values for the assembly line operations are shown below.


Assembly Line/
Operation
2- Shutdown
2- Partial Capacity
2- Full Capacity
1- Shutdown 0.02 0.06 0.05
1-Partial Capacity 0.07 0.14 0.20
1- Full Capacity 0.06 0.21 0.19

For example, the probability that the first assembly line is shut down and the second one is operating at partial capacity is 0.06.

What is the probability that:

A. both assembly lines are shut down? 0.02
B. neither assembly line is shut down? 0.74
C. at least one assembly line is at full capacity? 0.71
D. exactly one assembly line is at full capacity? 0.52
E. both lines are at full capacity conditional on neitherline being shut down? 0.26