3-1,3-2, 3-3,3-4 Experiment – the activity taking place – EX: rolling dice, drawing cards, flipping coins, etc. Outcome - What might happen when an experiment takes place - Ex: rolling a three, drawing an Ace of Hearts, tails on a coin, etc. Sample space - the set of all possible outcomes Event – A subset of the possible outcomes that contains the desired outcomes Probability of an event P(E) = number of ways that event may occur total number of all possible outcomes Equally likely outcomes; No outcome is more likely to occur than any other possible outcome. The complement of event A, denoted A , consists of all outcomes in which event A does not occur. P(not A) = __________________ A. Roll one die List the sample space: Find each probability: P(4) = P (not 4) = P(7) = P(number less than 7) = P(odd) = The probability of an impossible event is ______. The probability of an event that is certain to occur is _______. If a year is selected at random, find the probability that Thanksgiving Day will be on a (a) Wednesday , (b) Thursday . Every probability is a number between 0 and 1 . P(A or B) = P(event A occurs or event B occurs or they both occur) Use the data in the following table, which summarizes results from the sinking of the Titanic. Survived Died Men 332 1360 Women 318 104 Boys 29 35 Girls 27 18 If one person is randomly selected, find the probability : 1. P(women or a child) = 3. P( a child or someone who survived) 2. P( a man or someone who survived)= P(A and B) = P(event A occurs in a first trial and event B occurs in a second trial) Two cards are to be drawn with replacement. P(Ace and king) = P(Ace and Ace) = P(Ace and not Ace) = P(club and spade) = Two cards are to be drawn without replacement. P(Ace and king) = P(Ace and Ace) = P(Ace and not Ace) = P(club and spade) = Notation for Conditional Probability: P( B A) represents the probability of event B occurring after it is assumed that event A has already occurred. Given that Event 2 has occurred, you must make an adjustment to you sample space. The size of the sample space (total number of outcomes) will be reduced based on the knowledge that E2 has occurred. Conditional probability is written P(E1|E2) - read probability of E1 given E2. Examples: 1. Using tree diagrams: A family plans to have three children. Make a tree diagram for the sample space. Determine the following probabilities: P(at least two girls) P(at least two girls|the first child is a girl) P(exactly two boys) P(exactly two boys|at least one boy). P(three girls) P(three girls|first child is a girl) 2. Using a chart: A recent survey of Chipola students indicates the following results for type of soda preferred : Regular Cola Diet Cola No Cola Freshmen 40 30 15 Sophomores 30 30 20 Determine the following probabilities: P(cola) P(freshman) P(freshman or prefers cola) P(freshman and prefers cola) P(prefer regular cola|freshman) P(diet cola|sophomore) P(sophomore|prefer diet cola) Homework : Do Statistics Worksheet – Review of Probability