ABSTRACT
At the end of this chapter, you should be able to:
• define probability • define expectation, dependent event, independent event and conditional probability • state the addition and multiplication laws of probability • use the laws of probability in simple calculations • use the laws of probability in practical situations • determine permutations and combinations
The probability of something happening is the likelihood or chance of it happening. Values of probability lie between 0 and 1, where 0 represents an absolute impossibility and 1 represents an absolute certainty. The probability of an event happening usually lies somewhere between these two extreme values and is expressed either as a proper or decimal fraction. Examples of probability are:
that a length of copper wire has zero resistance at 100◦C 0
that a fair, six-sided dice will stop with a 3 upwards 16 or 0.1667
that a fair coin will land with a head upwards 12 or 0.5
that a length of copper wire has some resistance at 100◦C 1
If p is the probability of an event happening and q is the probability of the same event not happening, then the total probability is p +q and is equal to unity, since it is an absolute certainty that the event either does or does not occur, i.e. p+q=1
The expectation, E , of an event happening is defined in general terms as the product of the probability p of an event happening and the number of attempts made, n, i.e. E=pn.
