while 0.9 would signify a high probability.
Origins of probability
The mathematical theory of probability came to the fore in the 17th century
with discussions on gambling problems between Blaise Pascal, Pierre de Fermat
and Antoine Gombaud (also known as the Chevalier de Méré). They found a
simple game puzzling. The Chevalier de Méré’s question is this: which is more
likely, rolling a ‘six’ on four throws of a dice, or rolling a ‘double six’ on 24
throws with two dice? Which option would you put your shirt on?
The prevailing wisdom of the time thought the better option was to bet on the
double six because of the many more throws allowed. This view was shattered
when the probabilities were analysed. Here is how the calculations go:
Throw one dice: the probability of not getting a six on a single throw is ⅚,
and in four throws the probability of this would be ⅚ × ⅚ × ⅚ × ⅚ which is(⅚)^4.
Because the results of the throws do not affect each other, they are ‘independent’
and we can multiply the probabilities. The probability of at least one six is
therefore
1 − (⅚)^4 = 0.517746...
Throw two dice: the probability of not getting a double six in one throw is
35/36 and in 24 throws this has the probability (35/36)^24.
The probability of at least one double six is therefore
1 − (35/36)^24 = 0.491404...
We can take this example a little further.
Playing craps
The two dice example is the basis of the modern game of craps played in
casinos and online betting. When two distinguishable dice (red and blue) are
thrown there are 36 possible outcomes and these may be recorded as pairs (x,y)
and displayed as 36 dots against a set of x/y axes – this is called the ‘sample
space’.