Probability Introduction Precalc 4/20/12

Vocabulary  Probability – the chance that a particular outcome or event will occur.  It can be written as a decimal between 0 and 1, or a percent between 0% and 100%.  Equally likely – when multiple outcomes all have the same probability of occuring.  Example: When rolling a die, getting a 1,2,3,4,5, or 6 are all equally likely.  Disjoint – 2 or more events that cannot both occur at once.  Example: In 2012, your birthday could fall on a weekend or a weekday, but not both.

Notation & Vocabulary  P(x) = the probability that event “x” will occur.  Example: P(rain) is the probability that it will rain.  Complement of “x” – all of the outcomes that are not “x”  x’ – Complement of “x”  This means event x does not occur.  P (x’) = the probability that event x will not occur.  Example: When rolling a die, P(even’) is the probability that you will roll a number that is not even.

Calculating Probability  When all events are equally likely, P(x) = the number of ways for x to occur the total number of possible outcomes

Example: Equally likely outcomes  You have a box of pencils. There are: 6 orange pencils 4 red pencils 9 blue pencils, and 1 green pencil.  What are 2 disjoint events?  If you choose a pencil randomly, what is the probability that it is orange?  P(orange) =  6/ 20 = 3/10 =.3 = 30%

Calculating Probability: Disjoint outcomes  When two events are disjoint, the probability of one or the other occurring is the sum of the probability of each one.  Example: P (orange or red) = P (orange) + P (red) = 6/20 + 4/20 = 10/20 = 50%  What is P (red or green)? P( red or green) = P (red) + P (green) = 4/20 + 1/20 = 5/20 = ¼ =.25 = 25%