Probability theory can be approached by using through:-
a) theoretical mathematics
b) empirical reasoning
Before we define what is meant by probability, we must extend our vocabulary by defining some important terms.
An experiment - set of rules governing an operation which is performed.
An outcome - the result realised after performing the experiment one time.
An event - combination of outcomes.
Flipping a single die
Consider the experiment defined by flipping a single die (half of a pair of dice) and observing which of the six faces is at the top when the die comes to rest (notice how precise we are being. If you simply say 'flip a die', you could mean that you observe the time at which it hits the floor). There are six possible outcomes, these being any one of the six surfaces of the die facing upward after the performance of the experiment.
Consider the experiment defined by flipping a single die (half of a pair of dice) and observing which of the six faces is at the top when the die comes to rest (notice how precise we are being. If you simply say 'flip a die', you could mean that you observe the time at which it hits the floor). There are six possible outcomes, these being any one of the six surfaces of the die facing upward after the performance of the experiment.
There are many possible events (64 to be precise).
One event would be that of "an even number of dots" showing. This event is a combination of the three outcomes: two dots, four dots and six dots.
Another event is "one dot". This event is known as elementary event since it is the same as one of the outcomes.
Thus, out of the 64 possible events, six represents elementary events.
Food for thought - possible events and what are the odds??
Food for thought - possible events and what are the odds??
- Be killed in a terrorist attack while travelling (1 in 650,000).
- Die — during an average lifetime — of flesh-eating disease (1 in one million).
- Be killed by lightning (1 in 56,439).
