Warm Up 1. Ingrid is making dinner. She has tofu, chicken and beef for an entrée, and French fries, salad and corn for a side. If Ingrid has 6 drinks to choose from, how many meals can Ingrid create? 2. Tory is starting a business. He is choosing a vice president, marketing director and accountant from a pool of 13 applicants. How many ways could Tory create his executive team?

Answers 1. Ingrid is making dinner. She has tofu, chicken and beef for an entrée, and French fries, salad and corn for a side. If Ingrid has 6 drinks to choose from, how many meals can Ingrid create? 2. Tory is starting a business. He is choosing a vice president, marketing director and accountant from a pool of 13 applicants. How many ways could Tory create his executive team? 54 meals 1716 ways

Probability The likelihood that an event will happen Compare the chance that a specific event will happen to all the possible events that could happen

Some Terms! Probability: the likelihood that an event will occur Theoretical probability: what should happen Experimental probability: what actually happens in real life Outcome: the result of an experiment Sample Space: all the possible outcomes of an experiment Trial: one iteration of an experiment

Experiment: Rolling a die Outcomes: 1, 2, 3, 4, 5, and 6 Sample space: S = {1, 2, 3, 4, 5, 6}

Example 1 Consider this dartboard. Assume that the experiment is “throwing a dart” once and that the dart always hits the board. Find: a) The outcomes b) The sample space

Another term! Event: an event is a specific type of outcome Examples of an event: 1.Die showing an even number 2.Picking an ace from a deck of cards

Example 2 If an experiment consists of tossing a coin three times and recording the results in order, find the sample space. (Find all possible outcomes). S = {HHH, HHT, HTH, HTT, THH, THT, TTH, TTT}

The event E of showing “exactly two heads” consists of all outcomes with two heads. Write out that possible event. E = {HHT, HTH, THH} Example 2 Continued

What is the event F of showing at least two heads? F = {HHH, HHT, HTH, THH} What is the event G of showing no heads? G = {TTT} Example 2 Continued

If you flip a coin, what is the theoretical probability that it lands with heads up? If you flip a coin, what is the theoretical probability that it lands with tails up? How would you find experimental probability? Example 3

If you roll a standard die, what is the theoretical probability that it lands with the 3 facing up? If you roll a standard die, what is the theoretical probability that it lands with the 3 or the 4 facing up? Example 4

Suppose we select, without looking, one marble from a bag containing 4 red and 9 purple marbles. What is the probability of selecting a red marble? Example 5

Example 6 What is the probability of getting a sum of 5 when you roll a pair of dice? (Hint: make a chart!)

Rolling a Pair of Dice

Example 7: Your Turn! What is the probability of choosing, at random, the ace of spades from a deck of 52 cards? What is the probability of choosing any ace from a deck of 52 cards? What is the probability of drawing a red card from a deck of 52 cards? What is the probability of drawing a club from a deck of 52 cards?

Probability of Multiple Events So far, we’ve been considering one event at a time. Now, we are going to consider the probability of multiple events.

Example 8 A five-card poker hand is drawn from a standard deck of 52 cards. What is the probability that all five cards are spades? How many events are there?

Probability of Multiple Events To find the probability of multiple events, use: THE FUNDAMENTAL COUNTING PRINCIPLE! Probability of the first event Keep doing this for all the events that occur Probability of the second event Probability of the third event

Example 9 A bag contains 20 tennis balls, of which four are defective. If two balls are selected at random from the bag, what is the probability that both are defective?