Listing Outcomes and Expected Frequency

“Listing outcomes” refers to the various possible results that can come from performing a statistical or probabilistic event. This is a common method for theoretically analysing events and can be used in relatively simple events where the number of outcomes can be easily determined.
When listing outcomes of an event, it is important to make sure each outcome is mutually exclusive. This means that only one outcome can occur at any given time. For example, when tossed, a coin can either land on heads or tails, but not both simultaneously.
There are multiple methods to list outcomes, including tables, tree diagrams and diagrams known as ‘Venn diagrams’. The method used often depends on the complexity of the event being explored. For instance, if you are looking at the outcome of the toss of two dice, a table might be the simplest method.
A key aspect of statistics is the concept of ‘Expected Frequency’. This refers to the number of times you would expect an outcome to occur if the experiment was carried over a large number of times.
The Expected Frequency is calculated by multiplying the Total Number of Trials by the Probability of the Event. In real life situations where certain outcomes are sought, understanding expected frequency can be crucial.
A classic example of expected frequency is flipping a coin. If you flip a coin 100 times, you would expect it to land on heads around 50 times and tails around 50 times, as the probability for either is 0.5.
Remember that while expected frequencies give a solid theoretical understanding of what is likely to happen, actual outcomes in shorter sequences of events can deviate significantly due to chance.
Finally, ensure a clear understanding of the difference between experimental and theoretical probability. Theoretical probability is calculated through mathematical formulas, whereas experimental probability is determined by actually carrying out an experiment and recording the results.
Operations on compound events like “and” and “or” should also be addressed. Understand that for independent events, the probability of both events is the product of probabilities of each event. For mutually exclusive events, the probability of either event is the sum of the probabilities of each event.
You can further your understanding by working through a number of past paper questions, making sure to cover a variety of scenarios to ensure broad understanding. Be sure to understand why certain answers are correct, as this will help you tackle similar questions in the future.