Lab+5+Probability


 * EXERCISE 1: BERNOULLI TRIALS**
 * Bernoulli Trials Deffinition:** An experiment in which a single action, such as flipping a coin, is repeated identically over and over. The possible results of the action are classified as "success" or "failure". The binomial probability formula is used to find probabilities for Bernoulli trials.
 * Table of the frequency of RUNS in coin flips **
 * **HEADS ** || **TAILS ** ||
 * 1X12 || 1X7 ||
 * 2X3 || 2X6 ||
 * 3X4 || 3X3 ||
 * 4X2 || 4X1 ||
 * 5X1 || 5X5 ||


 * What is the __probability__ of getting heads or tails? **

//n// = number of trials //k// = number of successes //n � k// = number of failures //p// = probability of success in one trial //q// = 1 � //p// = probability of failure in one trial || The probability should be 1/2 for heads and 1/2 for tails, which means there should be a 50, 50 perecent chance for each. Judging from my graph there is an even distribution betwenn heads and tales except of one expception, and that is the amount of times the coin will turn up tails in a frequncey of 1.
 * [|Binomial Probability Formula]:
 * From your graph does it appear that there is any bias in the coin? **
 * EXERCISE 2: PROBABILITY WTIH MULTIPLE OUTCOMES (DICE)**
 * **Definition** || **Example** ||
 * **Experiment** is a situation involving chance or probability that leads to results called outcomes. || The experiment is throwing the dice. ||
 * **Outcome** is the result of a single trial of an experiment || Thepossible outcomes of landing on numbers 1-6. ||
 * **Event** is one or more outcomes of an experiment. || One event of this experiment is landing on 2. ||
 * **Probability** is the measure of how likely an event is. || The probability of land on 2 is ||


 * outcome || events || total # events ||
 * <span style="font-family: Arial,Helvetica;">1 || 23 || 4.35 ||
 * <span style="font-family: Arial,Helvetica;">2 || 20 || 5 ||
 * <span style="font-family: Arial,Helvetica;">3 || 19 || 5.26 ||
 * <span style="font-family: Arial,Helvetica;">4 || 10 || 10 ||
 * <span style="font-family: Arial,Helvetica;">5 || 13 || 7.7 ||
 * <span style="font-family: Arial,Helvetica;">6 || 15 || 6.66 ||


 * What are all the possible "events" when rolling a dice?** 1,2,3,4,5, and 6, or landing on and even or odd number.
 * <span style="font-family: Arial,Helvetica;">What are all the possible "outcomes" when rolling a dice? **<span style="font-family: Arial,Helvetica;"> Any number between 1-6, including 1 and 6.
 * <span style="font-family: Arial,Helvetica;">In 100 throws of the dice what is the probability that each number (outcomes) will occur? **<span style="font-family: Arial,Helvetica;">There is a 16.66% chance for each individual number.
 * <span style="font-family: Arial,Helvetica;">Is there any evidence that the dice was loaded? **<span style="font-family: Arial,Helvetica;">For the most the dice landed within the resonable range of their percentage except for maybe the number one, but that is not to concider it loade. It needs to have a much higher percentage for this to be even concidered and more consistant.
 * <span style="font-family: Arial,Helvetica;">EXERCISE 3: PROBABILITY WITH SUMS OF MULTIPLE OUTCOMES (PENNIES) **


 * <span style="font-family: Arial,Helvetica;">2 heads || 22 ||
 * <span style="font-family: Arial,Helvetica;">1 head + 1 tail || 53 ||
 * <span style="font-family: Arial,Helvetica;">2 tails || 25 ||
 * What percentage of the time is the outcome 2 heads?** 22%
 * <span style="font-family: Arial,Helvetica;">What percentage of the time is the outcome 2 tails? **<span style="font-family: Arial,Helvetica;">25%
 * <span style="font-family: Arial,Helvetica;">What percentage of the time is the outcome 1 head, 1 tail? **<span style="font-family: Arial,Helvetica;">53%
 * <span style="font-family: Arial,Helvetica;">Explain how you would calculate the probability for these results. **<span style="font-family: Arial,Helvetica;">I would multiply the individual outcomes, which would come out to be 1/3 X 1/3 X 1/3 because there are 3 possible outcomes for every time you flip.


 * <span style="font-family: Arial,Helvetica;">EXERCISE 4: PROBABILITY WITH SUMS OF MULTIPLE OUTCOMES (DICE) **
 * <span style="font-family: Arial,Helvetica;">What is the probability of each outcome for 1 dice? **<span style="font-family: Arial,Helvetica;">1/6
 * <span style="font-family: Arial,Helvetica;">What is the probability of each outcome for 2 dice? **<span style="font-family: Arial,Helvetica;">1/36
 * || <span style="font-family: Arial,Helvetica;">**1 (1/6)** || <span style="font-family: Arial,Helvetica;">**2 (1/6)** || <span style="font-family: Arial,Helvetica;">**3 (1/6)** || <span style="font-family: Arial,Helvetica;">**4 (1/6)** || <span style="font-family: Arial,Helvetica;">**5 (1/6)** || <span style="font-family: Arial,Helvetica;">**6 (1/6)** ||
 * <span style="font-family: Arial,Helvetica;">**1 (1/6)** || .04 || .04 || .03 || .02 || .01 || .03 ||
 * <span style="font-family: Arial,Helvetica;">**2 (1/6)** || .01 || 0 || .04 || .02 || .01 || .02 ||
 * <span style="font-family: Arial,Helvetica;">**3 (1/6)** || .04 || .04 || .03 || .03 || .04 || .04 ||
 * <span style="font-family: Arial,Helvetica;">**4 (1/6)** || .01 || .02 || .06 || .02 || .01 || .05 ||
 * <span style="font-family: Arial,Helvetica;">**5 (1/6)** || .05 || .01 || .03 || .03 || 0 || .01 ||
 * <span style="font-family: Arial,Helvetica;">**6 (1/6)** || .02 || .08 || .04 || .02 || .01 || .04 ||


 * <span style="font-family: Arial,Helvetica;">"Dice Probability" **
 * <span style="font-family: Arial,Helvetica;">2 || <span style="font-family: Arial,Helvetica;">3 || <span style="font-family: Arial,Helvetica;">4 || <span style="font-family: Arial,Helvetica;">5 || <span style="font-family: Arial,Helvetica;">6 || <span style="font-family: Arial,Helvetica;">7 || <span style="font-family: Arial,Helvetica;">8 || <span style="font-family: Arial,Helvetica;">9 || <span style="font-family: Arial,Helvetica;">10 || <span style="font-family: Arial,Helvetica;">11 || <span style="font-family: Arial,Helvetica;">12 ||
 * 1/19 || 1/19 || 1/12 || 1/19 || 11/36 || 8/13 || 19/36 || 2/13 || 7/36 || 1/13 || 1/19 ||

<span style="font-family: Arial,Helvetica;">**"Dice F****requency"**
 * <span style="font-family: Arial,Helvetica;">2 || <span style="font-family: Arial,Helvetica;">3 || <span style="font-family: Arial,Helvetica;">4 || <span style="font-family: Arial,Helvetica;">5 || <span style="font-family: Arial,Helvetica;">6 || <span style="font-family: Arial,Helvetica;">7 || <span style="font-family: Arial,Helvetica;">8 || <span style="font-family: Arial,Helvetica;">9 || <span style="font-family: Arial,Helvetica;">10 || <span style="font-family: Arial,Helvetica;">11 || <span style="font-family: Arial,Helvetica;">12 ||
 * 4 || 4 || 3 || 4 || 11 || 16 || 19 || 12 || 7 || 2 || 4 ||