A certain federal agency employs three consulting firms (A, B, and C) with probabilities of 0.40, 0.35, and 0.25, respectively. From past experience, it is known that the probability of cost overruns for the firms is 0.05, 0.03, and 0.15, respectively.
P(A) =0.40
P(B) =0.35
P(C ) =0.25
O = cost over run
P(O/A)=0.05
P(O/B)=0.03
P(O/C)=0.15
Baye’s theorem was used.
An a. What is the probability that this federal agency experiences a cost overrun?
P(O) = P(O/A)* P(A) + P(O/B)* P(B) + P(O/C)* P(C )
=0.05*0.40+0.03*0.35+0.15*0.25
=0.068
b. Suppose a cost overrun is experienced by the agency. What is the probability that the consulting firm involved is company C?
P(C/O) = P(O/C)* P(C ) / P(O)
=0.15*0.25 / 0.068
=0.551471
Probability is a branch of mathematics that quantifies the likelihood of an event occurring or the likelihood of a statement being true. The probability of an event is a number between 0 and 1, with approximately 0 indicating the improbability of the event and 1 indicating certainty.
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