Probability and Genetics
Before learning the AND and OR rules it is important to understand the concepts of an EVENT and an OUTCOME which are what these rules apply to. An event is any occurrence that you are studying such as the roll of a die, the toss of a coin, the birth of a child or the inheritance of an allele. An outcome is the specific result that occurs for an event, such as the number rolled on the die, whether a coin is heads or tails, if a child is male or female or if the dominant or recessive allele is inherited from a particular parent.
For an event, all possible outcomes must be mutually exclusive, that is, only one outcome can occur (you cannot roll both a 4 and a 6 on a single die, a coin cannot be both heads and tails, etc.). Each outcome has a probability associated with it which we will refer to as Pr(A) for outcome A of the event. For example, the probability of rolling a 5 is 1/6 for a 6-sided die. In the cases we study in our Genetics course it will be obvious what the probability of a particular outcome is; what we are really interested in is how to study the probability of different combinations of outcomes. This is what is covered in the links above.
One last thing: if you know every possible outcome for an event, the sum of their probabilities should be 1! If this is not the case then you are doing something wrong; either you have too few or too many outcomes counted or you have the individual probabilities wrong (or both).
The Wikipedia entry on probability