## How Many Possible Animals Are There?Consider just two animals (horse and giraffe) and three parts for each (head, body and legs).
## Probability of Making a Complete AnimalGiven eight different combinations, the chance of a complete giraffe being made is one chance out of eight. That is, we would expect one student out of every eight to create a complete giraffe. If there are 16 students in the class, we would expect two giraffes. If we had 24 students, we would expect three giraffes. If we had 200 people we would expect 25 giraffes. (This can be checked with the software using Option 4.)
Notice that although the actual number of giraffes is close to what is expected, it is not With three animals and 27 different combinations, the chance of getting a complete giraffe is 1 in 27. So, if we had 27 children in the group we would expect one complete giraffe (and also one horse and one duck). ## Natural VariabilityThe theoretical probability described above gives along-term prediction, that is, it tells us the average fraction of a very large number of crazy animals that will be one particular result. For relatively small numbers of rolls of the dice, like the single set of 200 in the picture above, this fraction cannot be expected to give the outcome.
## The Multiplication and Addition LawsThis investigation gives examples of these 'laws' in action. The laws are simply common sense rules that enable complex probabilities to be worked out from simpler ones.
^{1}/_{2} x ^{1}/_{2} x ^{1}/_{2}
These laws are really just common sense formalised.
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