0Introduction
IA Probability
0 Introduction
In every day life, we often encounter the use of the term probability, and they
are used in many different ways. For example, we can hear people say:
(i) The probability that a fair coin will land heads is 1/2.
(ii)
The probability that a selection of 6 members wins the National Lottery
Lotto jackpot is 1 in
19
6
= 13983816 or 7.15112 × 10
−8
.
(iii) The probability that a drawing pin will land ’point up’ is 0.62.
(iv)
The probability that a large earthquake will occur on the San Andreas
Fault in the next 30 years is about 21%
(v) The probability that humanity will be extinct by 2100 is about 50%
The first two cases are things derived from logic. For example, we know that
the coin either lands heads or tails. By definition, a fair coin is equally likely to
land heads or tail. So the probability of either must be 1/2.
The third is something probably derived from experiments. Perhaps we did
1000 experiments and 620 of the pins point up. The fourth and fifth examples
belong to yet another category that talks about are beliefs and predictions.
We call the first kind “classical probability”, the second kind “frequentist
probability” and the last “subjective probability”. In this course, we only
consider classical probability.