An event X can happen with probability P, and event Y can happen with probability P'. What is the probability that exactly one of them happens?

Options

A. `P+P'-2PP'`
B. `2PP'-P'+PP'`
C. `P-P'+2PP'`
D. `2P'P-P'+P`

Answer

To find the probability that exactly one of the events X or Y happens, we can break down the problem into two cases:

### Step 1: Define the events and their probabilities
- Let the probability of event X occurring be \( P \).
- Let the probability of event Y occurring be \( P' \).