Probability What are your Chances Overview Probability is

Probability: What are your Chances?

Overview Probability is the study of random events. The probability, or chance, that an event will happen can be described by a number between 0 and 1: • A probability of 0, or 0%, means the event has no chance of happening. • A probability of 1/2 , or 50%, means the event is just as likely to happen as not to happen. • A probability of 1, or 100%, means the event is certain to happen. **For instance, the probability of a coin landing heads up is ½, or 50%, This means you would expect a coin to land “heads up” half of the time.

Overview You can represent the probability of an event by marking it on a number line like this one Impossible 0 = 0% 50 – 50 Chance ½ , . 5, 50% Certain 1 = 100% The language of probability includes: • Experiment – a systematic investigation where the answer is unknown • Trial – one specific instance of an experiment • Outcome - the result of a single trial • Event – a selected outcome, such as getting an 11 from rolling two dice • Sample Space – the set of all possible outcomes of an experiment

Coin Toss Create a worksheet that looks like this. Toss a coin 25 times. Total the number of heads and tails. What percent was heads? Tails? Toss a coin another 25 times. Total the number of heads and tails for this trial. Add both trials together. Is there a difference in the percentage when you calculate 50 tosses versus 25 tosses?

Group Activity Part 1 Using 1 die or pieces of paper with the numbers 1 -6. Conduct a trial by rolling the die 100 times (or picking a piece of paper and returning it to the pile ). What do you think is the probability of picking a 1. How many times did you roll or pick 1, 2, 3, 4, 5, 6? What is the percentage for each number? Part 2 Combine your 100 rolls/picks with the 3 others in your group. What is the percentage for each number out of the now 400 rolls/picks? Submit a spreadsheet with this information, as well as a graph.

Describe a Situation 1. Describe a situation where the probability is ½. 2. Describe a situation where the probability is ¼. 3. Describe a situation where the probability is 5/9.

Probability

Make your own problem Here is a chance for you to design your own probability experiment. • What will you use? (dice, coins, colors) • What are all of the possible outcomes of the event? • Assign probabilities to the events using fractions or percent. • Make predictions.