Equally Likely Outcome
Equally likely outcomes are the possible results of a random experiment that have the exact same chance of occurring. In such experiments, there is no physical bias or reason to expect one outcome to happen more frequently than any other.
Key Concepts
The concept of equally likely outcomes forms the fundamental assumption for calculating theoretical probability in mathematics.
The standard probability formula can only be applied when all possible outcomes of the sample space are equally likely.
If a random experiment has 'n' equally likely outcomes, the probability of each individual elementary event occurring is exactly 1/n.
Formula & Equation
P(E) represents the theoretical probability of an event E occurring.
Common Misconceptions
Myth: Assuming that if an experiment has two possible outcomes, they must automatically be equally likely, such as thinking the chance of passing or failing a test is exactly 50/50.
Fact: Outcomes are only equally likely if the conditions are perfectly symmetric and unbiased. Passing a test depends on preparation and knowledge, making the outcomes not equally likely.
Real World Applications
Tossing a fair, unbiased coin where getting a Head and getting a Tail both have an exact 1/2 probability.
Rolling a standard six-sided die where landing on 1, 2, 3, 4, 5, or 6 each has an identical 1/6 chance of occurring.
Frequently Asked Questions
How do you know if outcomes are equally likely?
Outcomes are equally likely if the experiment uses fair, unbiased objects like a fair coin, an unbiased die, or a well-shuffled deck of cards where no specific result is favored.
Can we use the theoretical probability formula if outcomes are not equally likely?
No, the standard theoretical probability formula strictly requires all possible outcomes of the experiment to be equally likely. Otherwise, empirical probability must be used.