Probability What are your Chances? by Patricia Horrigan Rourke 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 •Event Space/or Sample Space – the set of all possible outcomes of an experiment Getting Started with Probability To get an overview of probability, click on the spinner and select the Introduction to Probability lesson. Read through the examples and take the quiz at the end. Make sure you are in slide show view then CLICK on the spinner 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? Play a Game Play Fish Tank and see if you can figure out the probability of getting a fish. 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. The Cereal Problem Use a computer simulation to find out how many boxes of cereal one would need to buy to get all 6 prizes. Make sure you set the number of prizes to 6. Make sure you are in slide show view then CLICK on the Cereal box Record the results of at least 10 trials to get an average of the trials. 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. 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 percents. Make predictions.