Probability 4

2. Relative Frequency Approach:   In practical life events are not equally likely  so we use Relative Frequency Approach  for this or we define Relative frequency as it is  another term for proportion; it is the value calculated by dividing the number of times an event occurs by the total number of times an experiment is carried out. The probability of an event can be thought of as its long-run relative frequency when the experiment is carried out many times. If an experiment is repeated n times, and event E occurs r times, then the relative frequency of the event E is defined to be rfn(E) = r/n Example Experiment: Tossing a fair coin 50 times (n = 50) Event E = 'heads' Result: 30 heads, 20 tails, so r = 30 Relative frequency: rfn(E) = r/n = 30/50 = 3/5 = 0.6 If an experiment is repeated many, many times without changing the experimental conditions, the relative frequency of any particular event will settle down to some value. The probability of the event can be defined as the limiting value of the relative frequency: P(E) = rfn(E)     A jar containing 12 red balls and 8 white balls The probability  of  getting red ball is  12/20 And probability of getting white balls is 8/20 Here occurrence of red balls is not equally likely than occurrence of White balls   3. Subjective Approach A subjective probability describes an individual's personal judgment about how likely a particular event is to occur. It is not based on any precise computation but is often a reasonable assessment by a knowledgeable person. Like all probabilities, a subjective probability is conventionally expressed on a scale from 0 to 1; a rare event has a subjective probability close to 0, a very common event has a subjective probability close to 1. A person's subjective probability of an event describes his/her degree of belief in the event. Example A Rangers supporter might say, "I believe that Rangers have probability of 0.9 of winning the Scottish Premier Division this year since they have been playing really well." Medical doctors sometimes assign subjective probabilities to the length of life expectancy for people having cancer.  Forecasting is another example of subjective probability.