Permutations & Combinations

Question

Part 1

Directions: Using a spinner, conduct an experiment to compare experimental probability with theoretical probability. 

Using a spinner you construct or a digital spinner, complete the following steps; write the probabilities as a fraction and a percentage.

1. What is the theoretical probability of spinning yellow?
2. What is the theoretical probability of spinning red or yellow?
3. Spin the spinner 20 times, create a table to display the results. What is the experimental probability of spinning yellow?
4. Perform another 20 spins, and record them. What is the new experimental probability of spinning yellow?
5. What is the experimental probability of spinning red or yellow? 
6. 

Part 2

Directions: Play a simple game of chance using a real die. Go to Mathwire.com and choose one of the seven dice games to play. Play the game three times, keeping a record sheet of the rolls and of successes, then answer the following questions.

Example datasheet:

Roll	Player 1	Player 2
1	6*	1*
2	1*	1
….
12	6	2*
….

*success

1. Using the data that was collected, determine the experimental probability of each outcome of the die over the course of the three games, and write as a fraction, decimal, and a percentage. 
2. Do you think dice games are fair? 
3. What conclusions do you draw now that you have collected data on a dice game?

Answer 1

What are the colors in the spinner besides red and yellow?

Suppose for example there are 10 colors: red, yellow, green, blue, orange, purple,

brown,black,white, and gold.

Then each color THEORETICALLY has 1/10 chance of appearing on any given spin.

So when the experiment is repeated 20 times, each color is EXPECTED to appear twice,

as 20 * 1/10 = 2

Of course, if actually do the experiment 20 times, it is unlikely that each color

will appear exactly twice. For example, green may appear only once, and yellow three times.

In this case, the EXPERIMENTAL probability is 1/20 and 3/10 respectively.

However, if you repeat the experiment 2 million times, you will see about

200,000 instances of each color.

This is called the LAW OF LARGE NUMBERS, which states that the more frequently you

perform the experiment, the EMPRIRICAL or EXPERIMENTAL probability shall get closer

to the EXPERIMENTAL probability.

Now, for the dice, the THEORETICAL probability of each of the six values is 1/6.

For a TWO dice game, I would recommend using the following model

1 2 3 4 5 6

----------------------------------

1 | 2 3 4 5 6 7

2 | 3 4 5 6 7 8

3 | 4 5 6 7 8 9

4 | 5 6 7 8 9 10

5 | 6 7 8 9 10 11

6 | 7 8 9 10 11 12

the row across the top represents the first die..

the column on the left represent the second die...

So the probability of rolling a sum of 7 is 6/36 = 1/6

because there are six ways to get a sum of 7 : (1,6), (2,5),(3,4)(4,3)(5,2)(6,1)

and there are 6*6=36 possibilities altogether

Since you did not give enough particulars and specifics about the rules of

the game(s) you have selected this is the best we can do for now.

Please repost with ONE PROBLEM per posting, with a COMPLETE description

and statement of the problem.

Thank you