A company believes there is a 20% chance the file modifications will be easy, a 40% chance that they will be moderately difficult and a 40% that they will be extremely difficult.Based on old files, modifications will be extensive or minor.Suppose the probabilities are as follows: P (Minor | Easy) = 0.80, P (Minor | Moderately Difficult)
= 0)50 and P (Minor | Extremely Difficult) = 0.20.What is the probability that the difficulty of the file modifications and transfer will be extremely difficult given that the consultant believes the modifications required are extensive?
A)0.57
B)0.20
C)0.32
D)0.44
E)0.90

Question

Quizplus · Accepted Answer

To find the probability that the difficulty of the file modifications will be extremely difficult given that the modifications required are extensive, we use Bayes' theorem. First, we need to calculate the probability of the modifications being extensive, P(Extensive), and then use it to find P(Extremely Difficult | Extensive).P(Extensive) = 1 - P(Minor)= 1 - [P(Minor | Easy)P(Easy) + P(Minor | Moderately Difficult)P(Moderately Difficult) + P(Minor | Extremely Difficult)P(Extremely Difficult)]= 1 - [0.80*0.20 + 0.50*0.40 + 0.20*0.40]= 1 - [0.16 + 0.20 + 0.08]= 1 - 0.44= 0.56Now, we calculate P(Extremely Difficult | Extensive) using Bayes' theorem:P(Extremely Difficult | Extensive) = [P(Extensive | Extremely Difficult) * P(Extremely Difficult)] / P(Extensive)Since P(Extensive | Extremely Difficult) = 1 - P(Minor | Extremely Difficult) = 1 - 0.20 = 0.80,P(Extremely Difficult | Extensive) = [0.80 * 0.40] / 0.56= 0.32 / 0.56= 0.57Therefore, the correct answer is A) 0.57.

A Company Believes There Is a 20% Chance the File