Probability is the possibility of the outcome of any random event. It is the measure of the likelihood of an event occurring. Many events cannot be predicted with total certainty, the chance of an event occurring can only be predicted.
Probability is expressed as a number between 0 and 1, where 0 indicates the event to be an impossible one and 1 indicates a certain event. The probability of an event A is represented by P(A). The probability of all events in a sample space adds up to 1.
Probability Terms and Definition
Sample space– the set of all the possible outcomes to occur in any trial.
Sample point– It is one of the possible results.
Experiment or Trial – A series of actions where the outcome is always uncertain.
Event – It is a single outcome of an experiment.
Outcome –Possible result of a trial/experiment.
Complementary event -The nonhappening events. The complement of event A is the event, not A ( or A1).
Impossible event- The event cannot happen.
Formula for Probability
The probability formula is defined as the possibility of an event happening being equal to the ratio of the number of favourable outcomes and the total number of outcomes.
Probability of event to happen P(E) = Number of favourable outcomes/ Total Number of outcomes.
For example, There are six pillows on a bed, 3 are red, 2 are yellow, and 1 is blue. What is the probability of picking a yellow pillow?
Answer: The probability is equal to the number of yellow pillows in the bed divided by the total number of pillows 2/6 =1/3.
Types of Probability
There are three major types of probabilities.
- Theoretical
- Experimental
- Axiomatic
Theoretical – this is based on the possible chances of winning. If a coin is tossed, the theoretical probability of getting the head will be half(1/2).
Experimental -this is based on the observation of an experiment. The calculation is based on the number of possible outcomes by the total number of trials. For example, if a coin is tossed 10 times and the head is recorded six times, then the experimental probability for heads is 6/10 or 3/5.
Axiomatic – a set of rules or axioms. The chances of occurrence or non-occurrence of the events can be quantified.
Conditional Probability –the likelihood of an event or outcome occurring based on the occurrence of a previous event or outcome.
Equally likely events – when events have the same theoretical probability of happening. For example, if you throw a die, the probability of getting 1 is 1/6.
Complementary Events – the possibility that there will be only two outcomes, which states that an event will occur or not. For example, it will rain or not rain today?
Major Application of Probability
- Weather forecasting or prediction of weather changes.
- Risk assessment and modelling in various industries.
- In the share market, chances of getting a hike in share prices.
- The probability of a team winning in a sport is based on players and the strength of the team.
