Sample Spaces and Probability CHAPTER 4.1

 “Life is a school of probability” ~ Walter Bagehot  “The only two sure things are death and taxes” ~ cynical philosopher  “Statistically, the probability of any one of us being here is so small that you'd think the mere fact of existing would keep us all in a contented dazzlement of surprise” ~ Lewis Thomas PROBABILITY

 Probability can be defined as the chance of an event occurring  A probability experiment is a chance process that leads to well-defined results called outcomes  An outcome is the result of a single trial of a probability experiment  A sample space is the set of all possible outcomes of a probability experiment PROBABILITY

ExperimentSample Space Toss one coin Roll a die Answer a true/false question Toss two coins EXAMPLES OF SAMPLE SPACE AND PROBABILITY EXPERIMENTS

 Find the sample space for rolling two dice SAMPLE SPACE

 Find the sample space for the gender of the children if a family has three children. Use B for boy and G for girl. SAMPLE SPACE

 A tree diagram is a device consisting of line segments emanating from a starting point and also from the outcome point. It is used to determine all possible outcomes of a probability experiment TREE DIAGRAM

MAKE A TREE DIAGRAM THE FAMILY WITH 3 CHILDREN

 An event consists of a set of outcomes of a probability experiment  An event with one outcome is called a simple event  A compound event consists of two or more outcomes or simple events EVENT

1.Classical or theoretical 2.Empirical or Relative frequency or Experimental 3.Subjective THE THREE TYPES OF PROBABILITY

 Classical probability uses sample spaces to determine the numerical probability that an event will happen. You do not actually perform the experiment to determine the probability.  Classical probability assumes that all outcomes in the sample space are equally likely to occur. CLASSICAL PROBABILITY

 The probability of any event E is the number of outcomes in E divided by the total number of outcomes in the sample space.  Denoted by FORMULA FOR CLASSICAL PROBABILITY

 What is the probability that the sun will rise tomorrow?  What is the probability that Indiana Jones will come crashing through our window?  What is the probability of getting heads when a coin is flipped? RANGE OF VALUES FOR PROBABILITY

 Probabilities should be expressed as reduced fractions or rounded to two or three decimal places.  When the probability of an event is an extremely small decimal, round to the first nonzero digit after the decimal point.  For example: would be rounded to ROUNDING RULES

 Equally likely events are events that have the same probability of occurring.  For example, flipping a coin and getting heads or tails EQUALLY LIKELY EVENTS

1.P(3) 2.P(even) 3.P(odd) 4.P(prime) 5.P(4 or 5) 6.P(value less than 7) FIND THE PROBABILITY OF EACH EVENT USING A SINGLE DIE

1.P(jack) 2.P(heart) 3.P(black ten) 4.P(six of clubs) 5.P(3 or 6) 6.P(3 or diamond) FIND THE PROBABILITY FOR EACH EVENT USING A STANDARD DECK OF CARDS

 If a family had three children, find the probability that exactly two of the three children are girls.  Find the probability that at least one of the three children is a boy. GENDER OF CHILDREN