Question

Hi,

i want the solution of question 144.

Thanks.

2-7 Bayes' Theorem 2-142. Suppose that P(ATB)=0.6. P(A) = 0.4, and P(B) = 0.3. Determine P(BIA). 2-143. Suppose that P(AIB)=0.5, P(AI B') = 0.1, and P(B) = 0.7. Determine P(BIA). 2-144. Software to detect fraud in consumer phone cards tracks the number of metropolitan areas where calls originate each day. It is found that 1% of the legitimate users originate calls from two or more metropolitan areas in a single day. However, 35% of fraudulent users originate calls from two or more metropoli- tan areas in a single day. The proportion of fraudulent users is 0.02%. If the same user originates calls from two or more metro- politan areas in a single day, what is the probability that the user is fraudulent?

Answer 1

100 The proportion of fraudent users is 0.02% So the proportion of legitimate user is C100-0-02) -99.98%, het, Å and B be the event of fraudent usen and legitimate were respectively. So, PCA) - se me = love p (6) - 99.98-9998 3 Toooo Lets y be the event of originating calls from two or more metropolitan areas. Now, Probability of originating ratina calls t calls from two or more metropolitan areas given that the user is legitimate= P(x/B) = 160 .. Probability of originating calls from two or more metropolitan areas given that users is fraudend = P(x1A) - Moo : .. Probability that the user is frondent given that the user originates from two on more metropoliton areas is - CPCAJ PG[4) PA/x) = PCA) PAIA) + PC® PZTB. 20.00695