Question

Question 9. 9. The probability of either, but not both, of two independent events occurring is the sum of their individual probabilities. (Points : 1)

True
False

Answer 1

If events are independent:


`P\left( A\cap B \right) =P\left( A \right) * P\left( B \right)`

*This would actually produce a tangible value not equal to 0 if events are independent.

Now:


`P\left( A\cap B \right) =P\left( A \right) +P\left( B \right) -P\left( A\cup B \right)`

Let's combine these two formulas in order to figure out whether your premise is true or false.


`P\left( A \right) +P\left( B \right) -P\left( A\cup B \right) =P\left( A \right) * P\left( B \right) \\ \\ \therefore \quad P\left( A\cup B \right) =P\left( A \right) +P\left( B \right) -P\left( A \right) * P\left( B \right)`

This means that the premise is false.