11ABexperimental

= Calculating Probability =

Experimental Probability

 * ** Experimental Probability ** is an estimate of the probability of an outcome based on the number of times that outcome has occurred in previous experiments


 * Experimental Probability can be calculated using:

math . \qquad \qquad Pr(A) = \dfrac{n(A)}{n(\varepsilon)} math
 * where n(A) is the number of times that A has occurred
 * and n( E ) is the total number of times the experiment has been carried out


 * ** Example 1 **
 * At a music festival, they took note of the gender of the people passing through a gate.
 * The results were MFFF MFMF FMFM MFFF FMMF MFFF FMFF F
 * Based on these observations, what is the probability that the next person is Female (F)
 * State answer correct to two decimal places
 * ** Solution **
 * n(F) = 19
 * n( E ) = 29

math . \qquad \qquad Pr(F) = \dfrac{19} {29} = 0.66 math

Theoretical Probability

 * ** Theoretical Probability ** is the probability of an outcome based on theory depending on the number and proportion of the possible outcomes.


 * Theoretical Probability can be calculated using:

math . \qquad \qquad Pr(A) = \dfrac{n(A)}{n(\varepsilon)} math
 * where n(A) is the proportional number of possible outcomes that represent A
 * and n( E ) is the total number of possible outcomes


 * ** Example 2 **
 * A bag contains a total of 24 marbles. Out of those, 7 are blue.
 * If we randomly draw one marble out of the bag, what is the probability that it is blue?


 * ** Solution **
 * n(Blue) = 7
 * n( E ) = 24

math . \qquad \qquad Pr(Blue) = \dfrac{7} {24} = 0.66 math

Games and Fair Games

 * In probability theory, a ** Game ** is any situation where two or more people compete against each other in such a way that there is only one winner.


 * A ** Fair Game ** is a game where each player has an equal chance of winning.


 * If the game is not fair, then it will be biased towards one of the players.


 * ** Example 3 **
 * Two people play a game which involves rolling a single dice.
 * If the dice produces 1 or 2, then player A wins
 * If the dice produces any other number, then player B wins
 * Is this a fair game?


 * ** Solution **

math . \qquad \qquad Pr(A wins) = \dfrac{2} {6} = \dfrac{1}{3} math

math . \qquad \qquad Pr(B wins) = \dfrac{4} {6} = \dfrac{2}{3} math

.
 * The chances of each player winning are not the same so this is __not__ a fair game.
 * This game is __biased__ towards player B

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