Answer:
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 :
![P(E_2/A)=\frac{P(E_2)\times P(A/E_2)}{P(E_1)\times P(A/E_1)+P(E_2)\times P(A/E_2)}](https://tex.z-dn.net/?f=P%28E_2%2FA%29%3D%5Cfrac%7BP%28E_2%29%5Ctimes%20P%28A%2FE_2%29%7D%7BP%28E_1%29%5Ctimes%20P%28A%2FE_1%29%2BP%28E_2%29%5Ctimes%20P%28A%2FE_2%29%7D)
![=\frac{(0.999869)(0.3)}{(0.000131)(0.03)+(0.999869)(0.3)}](https://tex.z-dn.net/?f=%3D%5Cfrac%7B%280.999869%29%280.3%29%7D%7B%280.000131%29%280.03%29%2B%280.999869%29%280.3%29%7D)
![\frac{0.2999607}{0.00000393+0.2999607}](https://tex.z-dn.net/?f=%5Cfrac%7B0.2999607%7D%7B0.00000393%2B0.2999607%7D)
![\frac{0.2999607}{0.29996463}](https://tex.z-dn.net/?f=%5Cfrac%7B0.2999607%7D%7B0.29996463%7D)
= 0.999986898 ≈ 0.999987
The ratio 11:4 means that the total number of spaces is a multiple of 15 parts, this multiple is what value is assigned to each part.
450/15=30 so each part is equal to 30 spaces
Full sized car spaces are 11*30=330 spaces
Compact car spaces are 4*30=120 spaces.