Respuesta :
Answer:
(a) 0.50
(b) 0.75
(c) 0.6522
Step-by-step explanation:
We are given that the firm’s management initially had a 50–50 chance of getting the project.
Let Probability of getting a project or bid being successful, P(S) = 0.50
Probability of not getting a project or bid being unsuccessful, P(US) = 1 - 0.50 = 0.50
Also, Past experience indicates that for 75% of the successful bids and 40% of the unsuccessful bids the agency requested additional information which means;
Let event R = agency requested additional information
So, Probability that the agency requested additional information given the bid was successful, P(R/S) = 0.75
Probability that the agency requested additional information given the bid was unsuccessful, P(R/US) = 0.40
(a) Prior probability of the bid being successful = Probability of getting a project or bid being successful = [tex]\frac{50}{100}[/tex] = 0.50
(b) The conditional probability of a request for additional information given that the bid will ultimately be successful = P(R/S) = 0.75
(c) The posterior probability that the bid will be successful given a request for additional information is given by P(S/R) ;
Using Bayes' Theorem for this we get;
P(S/R) = [tex]\frac{P(S) * P(R/S)}{P(S)*P(R/S) + P(US) * P(R/US)}[/tex] = [tex]\frac{0.50 * 0.75}{0.50*0.75 + 0.50*0.40}[/tex] = 0.6522 .
