15.1 Introduction to Probability ©2002 by R. Villar All Rights Reserved

Introduction to Probability The Probability of an event occurring is a number between 0 and 1. 0 means that the event cannot occur… 1 means that the event is certain to occur. If an event can succeed in s ways and fail in f ways, then the probabilities of success, P(s), and of failure, P(f), are as follows. P(s) = s P(f) = f s + fs + f If P(s) = 1, then the event is certain to succeed and P(f) = 0 If P(f) = 1, then the event is certain to fail and P(s) = 0 If an event is equally like likely to succeed as it is to fail, then P(s) = 1/2 and P(f) = 1/2 A variation of the probability formulas above is as follows: The probability of an event A will occur is P(A) = number of outcomes in A total number of outcomes

= 1 6 Example: You roll a six-sided die whose sides are numbered from 1 through 6. Find the probability of a. rolling a 4 b. rolling an odd number c. rolling a number less than 7 = number of ways to roll a 4 number of ways to roll the die = number of ways to roll an odd number number of ways to roll the die = 3 6 = 1 2 = number of ways to roll less than 7 number of ways to roll the die = 6 6 = 1

G EOMETRIC P ROBABILITY Some probabilities are found by calculating a ratio of two lengths, areas, or volumes. Such probabilities are called geometric probabilities.

Using Area to Find Probability You throw a dart at the board shown. Your dart is equally likely to hit any point inside the square board. Are you more likely to get 10 points or 0 points?

Using Area to Find Probability S OLUTION P (10 points) = area of smallest circle area of entire board Are you more likely to get 10 points or 0 points? π = = = ≈ π π 36 P (0 points) = area outside largest circle area of entire board 18 2 – (π 9 2 ) 18 2 = = = ≈ – 81π 4 4 – π You are more likely to get 0 points.