Probability

Study guides: Exam P-1, Exam FAM, Exam ALTAM, Exam ASTAM, Exam MAS-I

A Probability P is a measure of how likely an event E is to occur. It is a Set Function that maps events in a sample space to a real number between 0 and 1, and must satisfy the Axioms of Probability.

• If all outcomes in a finite sample space S are equally likely, then P can be calculated as:

P(E) = \frac{|E|}{|S|}

=\frac{\text{number of outcomes in E}}{\text{number of possible outcomes}}

Probability of a Fair Die?

What is the probability of rolling an even number on a fair 6-sided die?

Answer

• Sample Space (S): \{1, 2, 3, 4, 5, 6\}
• Event (E): Rolling an even number \rightarrow \{2, 4, 6\}

The size of the set S is 6 (there are 6 possible outcomes). The size of the set E is 3 (there are 3 even numbers)

• P(E) = \frac{|E|}{|S|} = \frac{3}{6} = 50\%

Common Trap Always verify the sample space first. If the problem said "a die is rolled and the result is greater than 2," your |S| would change from 6 to 4