Two events and are mutually exclusive if they cannot both happen at the same time. In other words, the existence of one excludes the existence of the other. An example is how tails and heads are mutually exclusive on a coin - if you got tails, you could not have gotten heads. Another example is when you toss a die, the event that you have an odd number is mutually exclusive from the event that you have an even one.

The probability of two independent events and are calculated by multiplying their individual probabilities:

Example: the probability of getting a king in a deck of cards is . The probability of getting a card of hearts is . Because the two probabilities are independent, the probability of drawing the king of hearts is: , as you would expect.

Complement is simply one minus the probability of the event. So if is an event with probability , then the probability of its complement is . The probability of getting a 4 on a die is . So the probability of not getting a 4, or the complement of the event that you get a 4 is: .

Hope that helps.