Ctrl+k

Calculate theoretical probability

Theoretical probability is the ratio of the number of favorable outcomes to the total number of equally likely outcomes in a finite sample space, expressed as a fraction, decimal, or percent between 0 and 1. The reasoning includes identifying an event, counting outcomes without double-counting, and interpreting 0 as impossible and 1 as certain; the scope is limited to simple equally likely situations, not conditional probability or more advanced probability models.

Detailed Explanation: Calculate theoretical probability

When all outcomes are equally likely, calculate theoretical probability with:

P(event)=number of favorable outcomestotal number of outcomesP(\text{event})=\frac{\text{number of favorable outcomes}}{\text{total number of outcomes}}
  • Favorable outcomes are the outcomes that match the event.
  • Total outcomes are all possible outcomes.
  • Count each outcome only once.

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

  1. List the total outcomes.
    A die can show:

1,2,3,4,5,61,2,3,4,5,6

There are 66 total outcomes.

  1. Identify the favorable outcomes.
    The even numbers are:

2,4,62,4,6

There are 33 favorable outcomes.

  1. Use the probability formula.

P(even number)=36P(\text{even number})=\frac{3}{6}

  1. Simplify the fraction.

36=12\frac{3}{6}=\frac{1}{2}

So, the probability of rolling an even number is:

12\boxed{\frac{1}{2}}

This is also 0.50.5 or 50%50\%. A probability of 00 means an event is impossible, and a probability of 11 means an event is certain.

Learn by doing: Calculate theoretical probability

Click a topic below to practice the foundational skills you'll need, learn the steps, or master this skill

    Practice with unlimited practice problems

    Probability - Shapes, Two Sets of One Shape, Two Colors - Pick Two by Color, To Decimal

      ?