Chapter 7-5Compound Events
Obj: To findthe probability of mutually exclusive events, and to find the probability of inclusive events
Why? - Can be used in health industries…for example to determine the likelihood of someone being color blind (ex 3, pg521)

OK….Lets sum up some old stuff and introduce some new terms before we move on…

Simple event – an event that describes a single outcome – example:

Compound Event – an event made up of two or more simple events –

In the world of probability, compound events are probabilities of two or more things happening at once. (We have already been doing this in some of our in class and homework problems )

For example: If you flip a coin and roll a die, what is the probability of getting tails and an even number….or -

These two events are called independent events because the outcome of one event does not affect the outcome of the other…and we learned

[Notice the use of the word “AND” – it means INTERSECTION - ∩]

MARBLESA bag contains 6 black marbles, 9 blue marbles, 4 yellow marbles, and 2 green marbles. A marble is selected, replaced, and a second marble is selected. Find the probability of selecting a black marble, then a yellow marble.

When the outcome of one event affects the outcome of another event, they are dependent events. In the above example, if the marble was not placed back in the bag, then drawing the two marbles would have been dependent events. The probability of drawing the second marble depends on what marble was drawn first….and we learned If two events, A and B, are dependent, then the probability of both events occurring is the product of the probability of A and the probability of B after A occurs….or

MARBLES…againNOW find the probability of selecting a black marble, then a yellow marble if the first marble is not replaced..

Mutually Exclusive Events - Events that cannot occur at the same time are calledmutually exclusive events. Suppose you wanted to find the probability of drawinga heart or a diamond. Since a card cannot be both a heart and a diamond, the eventsare mutually exclusive.

[Notice the use of the word “OR” – it means UNION - U]

MARBLES: A Bag contains 20 marbles: 8 Black, 7 Green, and 5 Blue. A marble is drawn from the bag at random. What are the chances of drawing a Black OR a Green Marble- and why are they mutually exclusive?

Example:A Drink Company applies one label to each bottle cap: “free drink”, “free meal”, or “try again”. A bottle cap has a probability of being labeled “free drink” and a chance “free meal”.

Why are the events “free drink” and “free meal” mutually exclusive?

What is the probability that a bottle cap is labeled “free drink” OR “free meal”?

Events that are NOT Mutually Exclusive, or Inclusive events, are events that have one or more outcomes in common. When you roll a single die, the outcomes “rolling an even number” and “rolling a prime number” are not mutually exclusive. The number 2 is BOTH prime and even, so the events are inclusive.

Or…

Inclusive Events -

Now lets consider the above situation…on a single roll of a die,what is the probability of “rolling an even number” or “rolling a prime number”…

More examples:
Find each probability on a die

Rolling a 5 or an odd number

Rolling AT LEAST one 4 when rolling 2 dice

A card is drawn from a deck of 52. Find the probability of each.

Drawing a king or a heart

Drawing a red card (hearts or diamonds) or a face card (jack, queen, king)

Checking for UNDERSTANDING

Homework 7.5 – pg 522, 2-10, 12-15