HotmathMath Homework. Do It Faster, Learn It Better.

Complement of an Event

If event Math formula is a subset of a sample space Math formula , the complement of Math formula contains the elements of Math formula that are not members of Math formula .  The symbol for the complement of an event Math formula is Math formula .

Example 1:

Consider the experiment of rolling a single die.
Math formula .  Let Math formula be the event that the roll yields a number greater than Math formula .  Math formula .  Then Math formula .

Remember: Math formula .  Math formula , so Math formula .  Since Math formula and Math formula are mutually exclusive , Math formula .  Therefore, Math formula

Example 2:

When it is not raining, the probability of the New Orleans Saints winning a football game is Math formula .  What is the probability of the Saints winning if it is raining?

Math formula (Saints winning with rain)

= Math formula Math formula (Saints winning without rain)

= Math formula

 

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