EZ Math

Statistics · Probability

How to Find the Probability of a Simple Event

Problem

an even number on one die\text{an even number on one die}

Answer

12\frac{1}{2}

Probability measures how likely an event is. List the outcomes, count the ones you want, then write the fraction.

Step-by-step solution

  1. Count the possible outcomes.

    1, 2, 3, 4, 5, 6⇒6 outcomes1,\ 2,\ 3,\ 4,\ 5,\ 6 \Rightarrow 6\ \text{outcomes}

    Why: A fair die has six equally likely outcomes.

  2. Count the favourable outcomes.

    2, 4, 6⇒3 outcomes2,\ 4,\ 6 \Rightarrow 3\ \text{outcomes}

    Why: Three outcomes are even numbers.

  3. Divide and simplify.

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

    Why: Probability is favourable outcomes over possible outcomes.

Common mistakes

  • Counting 1 as even. An even number divides by 2 with no remainder.
  • Writing 3/6 and stopping. Reduce the fraction.
  • Using the number of dice instead of the number of outcomes.

Practice problems

Use the same method. Work each problem on paper, then open the answer to check.

  1. rolling a 4\text{rolling a 4}

    Show answer

    16\frac{1}{6}

  2. rolling a number over 4\text{rolling a number over 4}

    Show answer

    13\frac{1}{3}

  3. heads on one coin toss\text{heads on one coin toss}

    Show answer

    12\frac{1}{2}

  4. a red ball, with 3 red and 2 blue\text{a red ball, with 3 red and 2 blue}

    Show answer

    35\frac{3}{5}

  5. rolling an odd number\text{rolling an odd number}

    Show answer

    12\frac{1}{2}