PLSC 751 - Probability and Relative Frequency

Suppose there are six faces on a dice. When we roll the dice and the number on the top of the dice is 1, we define this as a successful event. There are six different possible outcomes. The probability of success is:
                                   n/N = 1/6

Where n is the number of ways that are successful outcomes and N is the total number of events.

Example:
The probability of drawing an ace from a deck of 52 playing cards equals 4/52 = 1/13.

Definition:
The probability of an event is the proportion of time that the event will occur in the long run. Probability is the expected proportion of successful events.

Definition:
The relative frequency is the observed number of successful events for a finite sample of trials. Relative frequency is the observed proportion of successful events.

Example:
Suppose we toss a coin 50 times and have 27 heads and 23 tails. We define a head as a success. The relative frequency of heads is:
               n/N = 27/50 = 54%

The probability of a head is 50%. The difference between the relative frequency of 54% and the probability of 50% is due to small sample size.