Question

Assume you have a data set as below. It contains records of cars with three features: the type of the car (sports or SUV), the color of the car (red or yellow), and the origin of the car (domestic or imported). And the labels for the data are yes (car was stolen) and no (car was not stolen).

CarType,Color,Origin,Stolen?

sports,red,domestic,yes

sports,red,domestic,yes

sports,red,domestic,yes

sports,red,domestic,no

SUV,red,domestic,no

SUV,red,imported,yes

SUV,yellow,imported,no

SUV,yellow,imported,yes

SUV,yellow,domestic,no

sports,yellow,imported,no

sports,red,imported,yes

Calculate the probability of P(Yes|Red,Domestic,SUV)

Answer 1

Answer

we have to find the probability of yes given that it is a Red,Domestic,SUV car

let A and B be the events yes and Red,Domestic,SUV

then number of cars in (A and B) or number of cars in (yes and Red,Domestic,SUV) = 1 (because there is only one car which has yes and which is Red,Domestic,SUV)

total number of Red,Domestic,SUV cars = 2, i.e. P(B) = 2

using the formula P(A|B) = P(A and B)/P(B)

setting the values

P(A|B) = 1/2 or 0.5