Warm-Up In a class of 18 girls and 12 boys, what is the probability that a student raising his or her hand to answer a question is a girl?

Probability

Objective By the end of today’s lesson, I will learn and understand what a sample space is, and state sample spaces using tree diagrams and area models.

Things to consider The counting rules i.e., permutation, combination, and the fundamental counting principles we studied last week, can be combined with the probability rules in this unit to solve many types of probability problems. Probability is not a new concept to you because you took it up in late middle school. Probability can be defined as the chance of an event occurring. Many people are familiar with probability from observing or playing games of chance, such as card games, or lotteries. In addition to being used in games of chance, probability theory is used in the fields of insurance, investment, and weather forecasting and in various other areas. The basic concepts of probability are explained in this unit. These concepts include probability experiments, sample spaces, the addition and multiplication rules, and the probabilities of complementary events.

Basic Concepts Processes such as flipping a coin or drawing a card from a deck are called probability experiments.

Basic Concepts cont’d An outcome is the result of a single trial of a probability experiment

Basic Concepts cont’d A trial means flipping a coin once, or rolling a die once, etc.

Basic Concepts Cont’d A sample space is the set of all possible outcomes of a probability experiment

Now Test Your knowledge ExperimentSample Space Toss one coin Roll a dice Answer a true/false question Toss two coins State the sample space for each experiment.

ExperimentSample Space Toss one coinHeads, Tails Roll a dice1,2,3,4,5,6 Answer a true/false questionTrue, False Toss two coinsHead-Head, Head-Tail, Tail-Head, Tail-Tail Now Test Your knowledge State the sample space for each experiment.

Tree diagrams A tree diagram is a device consisting of the segments arising from a starting point and also from the outcome point. It is used to determine all possible outcomes of a probability experiment.