Chapter 16 – Understanding Probability and Long Term Expectations
Probability can be the estimation of our chances or personal beliefs.
Relative frequency interpretation is the probability that applies to situations where we can see the
results occurring over and over again. Probability is the relative frequency over the long run or the
proportion of times it occurs over the long run. Wouldn’t use a family with one boy and four girls and
say a 1/5 chance of getting a boy. We would use 1000 births and see the probability of having a boy as
the relative frequency.
To determine the probability of an outcome for relative frequency we can make an assumption about
the physical world. Things that give every possibility an equal chance can be assumed. Example: flipping
a coin, lottery chances. Does not necessarily mean it will happen exactly that many times per number of
tests. We can also observe the relative frequency through many repetitions of a situation. Sometimes
these are based on results from sample surveys.
Relative frequency can be applied to probability when a situation can be repeated and an outcome can
be observed. The relative frequency should become a constant value over the long run. This value is the
probability. It does not apply when the outcome is affected by something one time and another the next
time. Probability does not determine the outcome of a single occasion, just the long run. Relative
frequency is very useful for daily decisions.
Relative probability is limited to repeatable situations under the same conditions. Personal probability is
the interpretation of situations that may never happen again. Example: better mark in calculus or stats,
finding a parking spot. We assign personal probability to these situations based on our own knowledge
and experiences. Different people may not agree on the probabilities of different outcomes.
Personal probability is the degree to which an individual believes an event will happen. The probability
must be between 0 and 1 (0% and 100%). It must also be coherent, it doesn’t contradict the probability
of another event. We base a lot of decisions on personal probability. Example: committee decides what
candidates are appropriate for the job, jury