Bell Work

A card is drawn at random from the cards shown and not replaced. Then, a second card is drawn at random. Find each probability.

1. P(two even numbers)2. P(a number less than 4 and then a number

greater than 4)

7-3A&B Probability Experiments

Probability Simulation

A simulation is a way of modeling a problem situation, often ones that are difficult or impractical.

Today we will simulate purchasing a box of cereal and getting one of four possible prizes.

Conduct the Experiment

1. Place four different colored cubes into a paper bag.

2. Without looking, draw a cube from the bag, record its color, and then place the cube back in the bag.

3. Repeat steps 1 and 2 until you have drawn a cube from the bag a total of four times.

Analyze Your Results

1. Based on your results, predict the probability of getting each color.

2. What is the theoretical probability of getting each cube?

3. How do your probabilites in Exercises 1 and 2 compare?

4. Predict the probability of selecting all four colors in four boxes of cereal.

Rolling Doubles

1. Use the table to help you find the expected number of times doubles should turn up when rolling two number cubes 36 times.

2. Now roll the number cube 36 times. Record the number of times doubles turn up.

Analyze Your Results

1. Compare the number of times you expected to roll doubles with the number of times you actually rolled doubles.

2. What is the probability of rolling doubles out of 36 rolls using the number of times you expected to roll doubles from Step 1. The write the probability of rolling doubles out of the 36 rolls using the number of times you actually rolled doubles from Step 2.

Vocabulary

Theoretical Probability is based on what should happen when conducting a probability experiment.

Experimental Probability is based on what actually occurred during such an experiment.

*They may or may not be the same. As the number of times the experiment is conducted increase, the two should become closer in value.

Experimental Probability

When two number cubes are rolled together 75 times, a sum of 9 is rolled 10 times. What is the experimental probability of rolling a sum of 9?

Experimental and Theoretical Probability

The graph shows the results of an experiment in which a spinner with 3 equal sections is spun sixty times. Find the experimental probability of spinning red for this experiment.

Experimental and Theoretical Probability

Compare the experimental probability you found in example 2 to its theoretical probability.

You Try!

b. Refer to example 2. If the spinner was spun 3 more times and landed on green each time, find the experimental probability of spinning green for this experiment.

c. Compare the experimental probability you found in exercise b to its theoretical probability.

7-3D Fair and Unfair Games

Vocabulary

Mathematically speaking, a two-player games is fair if each player has an equal chance of winning.

A game is unfair if there is not such a chance.

Fair or Unfair?

In a counter-toss game, players toss three two-color counters. The winner of each game is determined by how many counters land with either the red or yellow side facing up. Play this game with a partner.

Fair or Unfair?

1. Player 1 tosses the counters. If 2 or 3 chips land red-side up, Player 1 wins. If 2 or 3 chips land yellow side up, Player 2 wins. Record the results in a table like the one shown below. Place a check in the winner’s column for each game.

2. Player 2 then tosses the counters and the results are recorded.

3. Continue alternating the tosses until each player has tossed the counters 10 times.

Analyze the Results

1. Make an organized list of all the possible outcomes resulting from one toss of the 3 counters.

2. Calculate the theoretical probability of each player winning.

3. Make a Conjecture Based on the theoretical probabilities of each player winning, is this a fair or unfair games? Explain your reasoning.

4. Calculate the experimental probability of each player winning. Write each probability as a fraction and as a percent.

5. Compare the probabilities in Exercises 2 and 4.

Fair or Unfair?

In a number-cube game, players roll two number cubes. Play this game with a partner.

1. Player 1 rolls the number cubes. Player 1 wins if the total of the numbers rolled is 5 or if a 5 is shown on one or both number cubes. Otherwise, Player 2 wins. Record the result sin a table like the one shown below.

2. Player 2 then rolls the number cubes and the results are recorded.

3. Continue alternating the rolls until each player has rolled the number cubes 10 times.

Analyze the Results

1. Make an organized list, or table, of all the possible outcomes resulting from one roll.

2. Calculate the theoretical probability of each player winning and the experimental probability of each player winning. Write each probability as a fraction and as a percent. Then compare these probabilities.

3. Make a Conjecture Based on the theoretical and experimental probabilities of each player winning, is this a fair or unfair game? Explain your reasoning.