Answer:
68.11% probability that the firm involved is firm B
Step-by-step explanation:
Bayes Theorem:
Two events, A and B.
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
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
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
What is the probability that the firm involved is firm B
68.11% probability that the firm involved is firm B