EQ: How can you calculate probabilities using number cubes, letter tiles, and spinners? Outcomes: the result of a single trial of an experiment.

Transcription

1 // Defining & representing Probability EQ: How can you calculate probabilities using number cubes, letter tiles, and spinners? Outcomes: the result of a single trial of an experiment. Experiment: situation involving chance that leads to results or outcomes. {1, 2, 3, 4, 5, 6} Sample Space: a list of all possible outcomes of an experiment enclosed in brackets { }, with commas between the outcomes. 1

2 16.1 Defining & representing Probability EQ: How can you calculate probabilities using number cubes, letter tiles, and spinners? Probability or rolling a head in an experiment. Event: one or a group of possible outcomes for a given situation. Probability of Event P(event) > P(heads) Tossing a Coin Simple Event: an event consisting of 1 outcome. Probability: measure of the likelihood that an event will occur. Assigns a numerical value to the chance that an event will occur. 2

3 16.1 Defining & representing Probability EQ: How can you calculate probabilities using number cubes, letter tiles, and spinners? P(even) = Probability of rolling an even number 1. List all possible outcomes > The possible even numbers that can be rolled are 2, 4, Add the number of outcomes > 3 possible outcomes of rolling an even number 3. Use the equation to determine the probability of rolling an even number. > P(even) = number of times an even can occur = 3» number of possible outcomes 6 3

4 16.1 Defining & representing Probability EQ: How can you calculate probabilities using number cubes, letter tiles, and spinners? Impossible Probability Scale = an event occurring is a number between 0 and 1. Written as percent, decimal or fraction As Likely As Not Certain 0 Unlikely 0.5 or ½ Likely 1 0% 50% 100% 4

5 16.1 Defining & representing Probability EQ: How can you calculate probabilities using number cubes, letter tiles, and spinners? Equally Likely: when probability of all outcomes of an experiment are EQUAL. 5

6 16.2 Determining Experimental Probability EQ: How is experimental probability different from the actual probability? Experimental probability is the ratio of the number of times an event occurs to the total number of trials performed. Answers the question: What does happen? 6

7 16.3 Determining Theoretical Probability EQ: How do you calculate theoretical probability and create an array to show all possible outcomes of the trials in each experiment? Heads Tails Theoretical probability: mathematical calculation that an event will happen in theory. Answers the question: What should happen The ratio of the number of desired outcomes to the total number of possible outcomes, or the sample space. 7

8 16.4 Simulating Experiments EQ: What type of simulation models fit certain situations? What percent of babies born at a hospital are girls? 50/50 Simulation: an experiment that models a real-life situation. One way to answer the question is to perform a simulation. When conducting a simulation, you must choose a model that has the same probability of the event. Trial: Each time you repeat an experiment or simulation. 8

9 / / Using Models for Probabililty EQ: How can you use tables and dot plots to construct and interpret probability models comparing experimental probabilities to theoretical probabilities to determine if the model is correct? Probability Model: a list of each possible outcome along with its probability. Usually shown in a table Sum of probabilities = 1 Sum of outcomes between 0 and 1 9

10 / / Using Models for Probabililty EQ: How can you use tables and dot plots to construct and interpret probability models comparing experimental probabilities to theoretical probabilities to determine if the model is correct? 5-choice multiple choice questions, each with 4 answers each. Uniform Probability Model: all the probabilities in a probability model are equally likely to occur. Weather forecast that predicts a 20% chance of rain, & 70% chance of no rain. nonuniform probability model: all probabilities in a probability model are not equivalent to each other. The sum of these two probabilities is 1, but the outcomes do not have the same probability. 10

11 / / Creating & Using Probability Models EQ: Can you use experimental data to create a probability model and then construct a second probability models using theoretical probabilities for comparison purposes? tree diagram: a tree-shaped diagram that illustrates the possible outcomes of a given situation. 11

12 / / Creating & Using Probability Models EQ: Can you use experimental data to create a probability model and then construct a second probability models using theoretical probabilities for comparison purposes? product being a multiple of 5 product not being a multiple of 5 Complementary Events: Events that consist of the desired outcomes and the remaining event that consist of all the undesired outcomes. Together- they include every possible outcome in the sample space 12

13 / / Determining Compound Probability EQ: When calculating the probability of compound events, can you tell the difference between those that use the word "and" and those that use the word "or"? Compound Events: Combines two or more events, using the word "and" or the word "or". AND: determining the probability of ONE event (multiply) OR: determining the probability for MORE THAN ONE event. > 1 event can occur or the other event can occur (add) 13

14 16.1 Defining & representing Probability EQ: How can you calculate probabilities using number cubes, letter tiles, and spinners? Independent Event: The occurrence of one event that has NO effect on the probability that a second event will occur. Dependent Event: The occurrence of one event that DOES have an effect on the probability that a second event will occur. > The second event is dependent on the first event. There are 3 red, 2 blue and 1 green Jolly Ranchers in the candy jar. Ben won the game and chooses a red Jolly Rancher. Noah got second place and chooses a Jolly Rancher from the remaining candy in the jar. 14