Respuesta :
Answer:
68.11% probability that the firm involved is firm B
Step-by-step explanation:
Bayes Theorem:
Two events, A and B.
[tex]P(B|A) = \frac{P(B)*P(A|B)}{P(A)}[/tex]
In which P(B|A) is the probability of B happening when A has happened and P(A|B) is the probability of A happening when B has happened.
In this question:
Event A: Cost overrun
Event B: Agency B used.
A certain federal agency employs three consulting firms (A, B and C) with probabilities 0.40, 0.45 and 0.15.
This means that [tex]P(B) = 0.45[/tex]
From past experiences, it is known that the probability of cost overruns for the firms are 0.01, 0.14, and 0.17, respectively.
This means that [tex]P(A|B) = 0.14[/tex]
Probability of cost overrun.
Firm A is used 40% of the time, with 1% of these having cost overrun. B is used 45%, with 14% of these having cost overruns. C is used 15% of the time, with 17% of these having cost overruns.
So
[tex]P(A) = 0.4*0.01 + 0.45*0.14 + 0.15*0.17 = 0.0925[/tex]
What is the probability that the firm involved is firm B
[tex]P(B|A) = \frac{0.45*0.14}{0.0925} = 0.6811[/tex]
68.11% probability that the firm involved is firm B
