Question

Suppose that 36 % of families living in a certain country own an SUV and 27 % own a truck. The addition rule might​ suggest, then, that 63 % of families own either an SUV or a truck. ​What's wrong with that​ reasoning?

Answer 1

P(SUV) = 0.36

P(Truck) = 0.27

P(Truck or SUV) = 0.63

This 0.63 is derived as P(SUV) + P(Truck) = 0.36 + 0.27 = 0.63

But, here the problem is that, if a family is owning both as SUV and a truck, that family is counted among SUVs, and among Trucks. When we add the probabilities, we add the same family twice. In probabilistic terms, P(SUV and Truck) is counted twice When you use addition rule.

Direct addition of probabilities to calculate P(A or B) is applicable only when the events are mutually exclusive that is when both events do not occur at the same time. SO, if no family is having both SUVs and Trucks, this addition is correct, but we cannot make that assumption. So, this reasoning is wrong.