Day 3 extra

Daily Objective- Students will be able to find the number of outcomes for compound events, identify independent and conditional events, and compute probability and odds.

Definitions-
Compound event- An event that consists of two or more events that are not mutually exclusive.
Independent event-An outcome that is not affected by previous outcomes.
Conditional event-An outcome that is affected by previous outcomes.
Probability- Is the measure of how likely an event is.
Odds- Is the ratio that compares the number of favorable outcomes of an event to the number of unfavorable out comes.

-HOW TO FIND THE NUMBER OF OUT COMES FOR COMPOUND EVENTS-

Consider two different events.  Rolling a six sided dice and spinning a 5 position game spinner.

First, determine the number of possible outcomes for each of the events.
     The dice has 6 possible outcomes.
     The spinner has 5 possible outcomes.
Next, multiply the outcomes together to get the total number of possible outcomes.
     6 * 5 = 30 possible outcomes.

-HOW TO IDENTIFY CONDITIONAL AND INDEPENDENT EVENTS-


The key to determining if an outcome or probability of an event has an affect on the outcome or probability of an event occuring.  For example if I have two dice and one outcome is to roll a 1 on each die we can see that if any one of the die is NOT a one, the probability that you will roll two ones is zero.  So, the event, rolling two ones, is dependent on one of the dice being a one.  Another example may help.  If you determine that 65% of bicycle owners have a mountain bike and that 20% of bicycle owners have a mountain bike with full suspension it is easy to see that the second event (mountain bikes with full suspension) is dependent on the event of having a mountain bike.

Independent events do NOT have any effect on the outcome or probability of each other.  A classic example of this is flipping a coin.  If I flip a coin, there is a 50% probability that it will come up heads.  Flipping the coin again, regardless of how many coin flips have proceeded it and what the outcome of those flips was does NOT change the probability of it coming up heads.  Each coin flip is therefore independent because the outcome and probability doesn't based on another event.

The question that must be answered is:  What other events will affect the outcome or probability of another event?  If the answer is NONE, then you have an Independent event - otherwise it is conditional.

-HOW TO CALCULATE PROBABILITY AND ODDS-

Simply defined, probability is the likelihood of a specific outcome for a given event. This can be calculated mathematically, generally as a percent, by giving the number of outcomes divided by the total number of possible outcomes.  We'll use rolling a dice as an example.

The probability of rolling a 6 on a six sided dice.  There is one 6 on the dice, so the number of specific outcomes is 1.  The total possible is 6.  The probability is 1/6 or 16.6666%.  If you change the specific outcome to rolling an even number, the number of specific outcomes is 3 and the total possible is 6.  Using our formula, 3/6 = 50% probability.

Odds are the first cousin of probability.  However, odds define the number of disireable outcomes vs the undesireable outcomes and is expressed as a ratio.

So, to determine odds, define the number of desired outcomes.  Then determine the number of undesirable outcomes.  Express this as ratio Desireable:Undesireable.

You go to a baseball game. The desirable outcome is getting a hit or a walk.  The undesirable is getting an out.  Now, lets say that this batters on base average (percentage of the time he gets a desirable outcome) is 40%.  This implies that 60% of the time he get an undesirable outcome.  Desirable (40)/Undesirable(60) results in a ratio 40:60, which reduces to 2:3.  The odds for this batter yielding a good result is 2:3.

QUIZ

1.  Calculate the number of outcomes for the following:  A dice with 6 sides and a spinner with 5 possible outcomes.

2.  Independent events do NOT have any affect on the outcome or probability of occurrence of each other.

               a) True

               b) False

               c) 50% chance of not never happening

3.  What is the probability of rolling either a 4 or a 6 on a six sided die.  Here is another great way to look at probabilities See video tutorial on probability.

Answer Key

1.  Multiply the number of possible outcomes of the each event by each other.  In this case there are 6 outcomes possible on the die and 5 for the spinner.

       6 x 5 = 30 possible outcomes.

2.  a) True.  Independent events are events that do NOT effect each other.

More about Independent events 

3.  Probability is calculated by dividing the number of desired outcomes by the total possible outcomes.  In this case, there are two desired outcomes: 4 or 6.  The total number possible is 6.

      2/6 = 1/3 = 0.33333 or 33.333% probability of rolling a 4 or a 6

More about probability