different concepts of probability

8/4/2019 Different Concepts of Probability

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DIFFERENT CONCEPTS OFPROBABILITY



WHAT IS P ROBABILITY

The relative possibility that an event will occur, asexpressed by the ratio of the number of actual

occurrences to the total number of possibleoccurrences.

It attempts to predict answers such as:What are the chances of you rolling 7 or 11 in a row?



EXAMPLE OF P ROBABILITY

If the weather report forecast a 90% chance of rain,there is still a slight possibility that sunny skies will

prevail. While there are no sure answers, in thiscase it probably will rain.



P ROBABILITY S CALE

We can look at probability on a scale from 0 - 1.0 - event never will occur

.5- the event and "not event" are likely to occur1- always will occur



WE ARE ABLE TO CALCULATE PROBABILITY IN TWO DIFFERENT SITUATIONS

The first being Experimental. Experimental probability iswhen data is collected and the probabilities arecalculated. For example, X and Y are playing Tic TacToe, they play 10 games and it was observed that Y won7 out of the 10 games, so the probability of Y winning is7 out of 10 or 70%.The second situation of probability is Theoretical.Theoretical probability are when results are predicted

using counting principles. For example, if X goes skiingand goes off a difficult jump 10 times you would expecthalf of the jumps for her to fall and the other half for herto land, so the probability of her to fall is 5 out of 10 or

50%.



TERMS Statistical Fluctuation: If the number of repetitions is small, the twoprobabilites can be different.Experiment: Probability problems involving repetition i.e. rolling a pair of

die or flipping a coinTrial: A step in a probability experiment in which an outcome is producedand tallied (each repetition is called a trial)Event: Grouped outcomes with something in commonProbability of an Event A, P(A): A quantified measure od the likelihood thatevent A will occur. The probability of an event is always a value between 0and 1Sample Space (S): The set of all possible outcomes in a probabilityexperimenti.e. If Player A draws a 1 and Player B draws 2, you can label this outcome(1,2) in this particular game the result is the same for the outcomes (1,2) and(2,1) but with different rules it might be important who draws whichnumber. So, it makes sense to view the two outcomes differently.

* Remember that the probability of P(A) is between 0 and 1The probability of an event A, P(A) is:P(A)= n(A)n(S)n(A)= # of ways event A can occur n(S)= total # of possible outcomesP(A')= probability of A not happening (compliment of A) P(A')= 1-P(A)



TYPES OF PROBABILITY Empirical: The number of times that an event occurs in an experiment divided by thenumber of trials. The empirical probability is also known as the experimental orrelative-frequency probability i.e if you had found that in the first ten trials, theproduct was greater than the sum four times, then the empirical probability of thisevent would be:

P(A)= 4

10

= 0.4

Theoretical: The probability of an event deduced from analysis of the possibleoutcomes. Theoretical probability is also called classical or a priori probability i.eWhat is the probability of flipping a coin 20 times and getting heads?As we all know their are two sides to a coin (a head and a tail) we are expected to getheads 10 times if we flip the coin 20 times. This would be half or 50% probability.Since for each time we flip the coin once thier is 1/2 chance of getting heads.

Subjective: An estimate of the likelihood of an event based on intuition andexperience (an educated guess) i.e estimate the probability thata) the next pair of shoes you buy will be the same size as the last pair you boughtSolution: there is a small chance that the size of your feet has changed significantlyor that different styles of shoes may fit you differently, so 80-90% would be areasonable subjective probability that your next pair of shoes will be the same as yourlast pair.



THANK YOU

different concepts of probability

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