Engineering Economic Analysis

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310 UNCERTAINTY IN FUTURE EVENTS

What are the probability distributions for the annual benefit and life for the following project?

The annual benefit's most likely value is $8000 with a probability of 60%. There is a 30%

probability that it will be $5000, and the highest value that is likely is $10,000. A life of 6 years

is twice as likely as a life of 9 years.

sOluTION ..

Probabilities are given for only two of the possible outcomes for the annual benefit. The third

value is found using the fact that the probabilities for the three outcomes must sum to 1, (Equa-

tion 10-3).

1 = P(Benefit is $5000) + P(Benefit is $8000) + P(Benefit is $10,000)

P(Benefit is $10,000) = 1 - 0.6 - 0.3 = 0.1

The probabilitydistributioncan then be summarizedin a table. The histogram or relativefrequency

diagram is Figure 10-1.

Annual benefit

Probability

$5000

0.3

$8000

0.6

$10,000

0.1

FIGURE 10-1 Probability distribution 0.7

for annual benefit.

0.6

0.5

.~:= 0.4

~~

£0.3

0.2

0.1

o

$5,000 $8,000 $10,000

Annual Benefit

The problem statement tells us:

P(lifeis 6 years)=2P(lifeis 9 years)

• 
  
  
  
  • Equation 10-3 can be applied to write a second equation for the two unknown probabilities:
  
  
  
  

P(6)+P£9)= 1