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Math Studies mini projects IB curriculum grid and planetqhe An Exemplar Project Template Project one - Chevalier de Mere 1 Project two - Chevalier de Mere 2 Project three - Birthdays Project four Monty Hall Design a distorted die

Name:

DAVID HARRIS

Experiment:

HEADS AND TAILS SIMULATION

STATEMENT OF TASK

There are three main schools of thought in the study of probability.

Subjective probability depends only on ones individual judgment of how likely and event is.

Experimental (or Empirical) probability measures are made from calculations based on observing the results of an experiment.

Theoretical (Classical) probability is derived objectively and with no reference to experiment from the number of and type of outcomes the experiment can give.

In this mini-project I aim to compare these three types of measure with reference to a simple probability experiment tossing a coin.

  DATA COLLECTION

Number of
heads

Experimental
probabilities

58

0.58

57

0.57

54

0.54

54

0.54

53

0.53

52

0.52

52

0.52

51

0.51

49

0.49

49

0.49

49

0.49

48

0.48

48

0.48

47

0.47

47

0.47

45

0.45

45

0.45

45

0.45

44

0.44

41

0.41

 

 

 

 

I simulated 20 sets of 100 coin flips.

 

The experimental probability was calculated with the formula

Experimental probability =

 

 

 

 

 

 

 

DATA ANALYSIS

 

0.58

 

0.57

 

0.54

 

0.54

 

0.53

Q3=0.525

0.52

 

0.52

 

0.51

 

0.49

 

0.49

Median=0.49

0.49

 

0.48

 

0.48

 

0.47

 

0.47

Q1=0.46

0.45

 

0.45

 

0.45

 

0.44

 

0.41

The median value of 0.49 gives the center of the data.

  CONCLUSION/EVALUATION

Subjectively it seems reasonable to state that a fair coin would have just as much chance of giving the outcome heads in an experiment as tails, but this is not exactly confirmed by the Experimental probability values which range from 0.41 to 0.58. However the median value is 0.49 and this is very close to the Theoretical probability value of 0.5.

 

Repeating the experiment would give more data, however the Subjective estimate would remain the same because the data so far does not give good reason to assume that the coin is baised. Another experiment would give another value for the median since in a random experiment like this it is unlikely to replicate the same 20 values. The Theoretical probability value would also remain constant.

 

It has to be also remembered that the results from the computer simulation only model the physical event of tossing a coin by use of the random number generator and so rest on the assumption that the computer has been programmed to do this authentically.