Lab+5+Probability

Bernoulli trial- " A random event that has three important characteristics. Its result must be a success or failure; the probability of a success must be the same for all trials, and the outcome of each trial must be independent of the other trial’s outcomes. A coin toss would meet the requirements of a Bernoulli trial."
 * EXERCISE 1: BERNOULLI TRIALS **

This definition is taken verbatim (I hope taking definitions verbatim and putting a source is okay, I just really did not know how to put this definition in my own words and still have it be truthful to the actual definition of a bernoulli) from: []

The probability of getting heads or tails is one out of two. From my chart, there is a slightly higher amount of the coin landing on the tails side of the coin than on the head, but overall I would not say this is bias.


 * Heads || Tails ||
 * 2x/5 || 2x/3 ||
 * 3x/4 || 3x/2 ||
 * 4x/ || 4x/2 ||
 * 5x/2 || 5x/ ||
 * 6x/ || 6x/1 ||
 * 7x/ || 7x/ ||
 * 8x/ || 8x/ ||

**EXERCISE 2: PROBABILITY WTIH MULTIPLE OUTCOMES (DICE) ** **An ****experiment** **is a situation involving chance or probability that leads to results called outcomes.** **a) So with dice, rolling the die is the experiment. **

**An ****outcome** **is the result of a single trial of an experiment.** **b) The outcomes of rolling a die would be that the dye lands on one of it's sides 1,2,3,4,5,6. **

**An ****event** **is one or more outcomes of an experiment.** **c) An event in rolling the die could be that it lands on 4. **

**Probability** **is the measure of how likely an event is.** d) The probability of the die landing on six is one sixth.

**These definitions are taken verbatim from: ** [|http://www.mathgoodies.com/lessons/vol6/intro_probability.htm]

In 100 throws of the dye, the probability of it landing on each number is 16.7%.
No, there is no evidence that the die was loaded.

**<span style="font-family: Arial,Helvetica;">EXERCISE 3: PROBABILITY WITH SUMS OF MULTIPLE OUTCOMES (PENNIES) ** Outcome 2 heads= 3.85% Outcome 2 tails= 3.57% Outcome one head one tail= 2.17% heads || 26 ||
 * Outcome || Events || Total Events ||
 * 1 || 17 || 100 ||
 * 2 || 13 || 100 ||
 * 3 || 23 || 100 ||
 * 4 || 14 || 100 ||
 * 5 || 16 || 100 ||
 * 6 || 17 || 100 ||
 * 2
 * 1 head + 1 tail || 46 ||
 * 2 tails || 28 ||

**<span style="font-family: Arial,Helvetica;">EXERCISE 4: PROBABILITY WITH SUMS OF MULTIPLE OUTCOMES (DICE) **

http://nces.ed.gov/nceskids/createagraph/graphwrite.asp?ID=666c6939c15e4725b93cd1a48ab8f9f0&file=png I believe y is supposed to be probability, and x is supposed to be frecuency, but for some reason the graph on create a graph would not let me change it. Sorry. <span style="font-family: Arial,Helvetica; font-size: medium; line-height: normal;">What is the probability of each outcome for 1 dice? There is a 1 out of 12 probability for each outcome. <span style="font-family: Arial,Helvetica; font-size: medium; line-height: normal;"> What is the probability of each outcome for 2 dice? <span style="font-family: Arial,Helvetica; font-size: medium; line-height: normal;">There is a 1 out of 36 probability for each outcome. The calculated probability The measured frequency
 * || <span style="border-collapse: separate; font-family: Arial,Helvetica; font-size: medium;">1 (1/6) || <span style="border-collapse: separate; font-family: Arial,Helvetica; font-size: medium;">2 (1/6) || <span style="border-collapse: separate; font-family: Arial,Helvetica; font-size: medium;">3 (1/6) || <span style="border-collapse: separate; font-family: Arial,Helvetica; font-size: medium;">4 (1/6) || <span style="border-collapse: separate; font-family: Arial,Helvetica; font-size: medium;">5 (1/6) || <span style="border-collapse: separate; font-family: Arial,Helvetica; font-size: medium;">6 (1/6) ||
 * ====<span style="border-collapse: separate; font-family: Arial,Helvetica; font-size: medium;">1 (1/6) ==== || ====1/36==== || 1/36 || 1/36 || 1/36 || 1/36 || 1/36 ||
 * <span style="border-collapse: separate; font-family: Arial,Helvetica; font-size: medium;">2 (1/6) || 1/36 || 1/36 || 1/36 || 1/36 || 1/36 || 1/36 ||
 * <span style="border-collapse: separate; font-family: Arial,Helvetica; font-size: medium;">3 (1/6) || 1/36 || 1/36 || 1/36 || 1/36 || 1/36 || 1/36 ||
 * <span style="border-collapse: separate; font-family: Arial,Helvetica; font-size: medium;">4 (1/6) || 1/36 || 1/36 || 1/36 || 1/36 || 1/36 || 1/36 ||
 * <span style="border-collapse: separate; font-family: Arial,Helvetica; font-size: medium;">5 (1/6) || 1/36 || 1/36 || 1/36 || 1/36 || 1/36 || 1/36 ||
 * <span style="border-collapse: separate; font-family: Arial,Helvetica; font-size: medium;">6 (1/6) || 1/36 || 1/36 || 1/36 || 1/36 || 1/36 || 1/36 ||
 * 2 || 3 || 4 || 5 || 6 || 7 || 8 || 9 || 10 || 11 || 12 ||
 * 1/36 || 2/36 || 3/36 || 4/36 || 5/36 || 6/36 || 7/36 || 8/36 || 9/36 || 10/36 || 11/36 ||
 * 2 || 3 || 4 || 5 || 6 || 7 || 8 || 9 || 10 || 11 || 12 ||
 * 1 || 1 || 2 || 2 || 3 || 3 || 4 || 4 || 5 || 5 || 6 ||