Software to detect fraud in consumer phone cards tracks the number of metropolitan areas where calls originate each day. it is found that 3% of the legitimate users originate calls from two or more metropolitan areas in a single day. however, 30% of fraudulent users originate calls from two or more metropolitan areas in a single day. the proportion of fraudulent users is 0.0131%. if the same user originates calls from two or more metropolitan areas in a single day, what is the probability that the user is fraudulent? round your answer to six decimal places (e. g. 98.765432).

0.999987

Step-by-step explanation:

Given that

The user is a legitimate one = E₁

The user is a fraudulent one = E₂

The same user originates calls from two metropolitan areas  = A

Use Bay's Theorem to solve the problem

P(E₁) = 0.0131% = 0.000131

P(E₂) = 1 - P(E₁)  = 0.999869

P(A/E₁) = 3%  = 0.03

P(A/E₂) = 30% = 0.3

Given a randomly chosen user originates calls from two or more metropolitan, The probability that the user is fraudulent user is :

= 0.999986898 ≈ 0.999987

the answer is a

step-by-step explanation:

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