Plans

Solved math examples

Probability: solved examples

Worked examples of probability, from easy to hard, with every step written out. Try each one yourself first, then check the working.

✓ Every answer here is computed and checked by the math engine

Easy

  1. Example 1. A bag has 5 red, 3 blue and 9 green counters. One counter is picked at random. What is the probability that it is blue?

    1. There are 3 blue counters out of 17.
      P(blue)=317P(\text{blue}) = \frac{3}{17}
    2. Simplify the fraction.
      =317= \frac{3}{17}

    Answer: 317\frac{3}{17}

  2. Example 2. A bag has 1 red, 3 blue and 2 green counters. One counter is picked at random. What is the probability that it is green?

    1. There are 2 green counters out of 6.
      P(green)=26P(\text{green}) = \frac{2}{6}
    2. Simplify the fraction.
      =13= \frac{1}{3}

    Answer: 13\frac{1}{3}

  3. Example 3. A bag has 8 red, 9 blue and 1 green counters. One counter is picked at random. What is the probability that it is green?

    1. There are 1 green counters out of 18.
      P(green)=118P(\text{green}) = \frac{1}{18}
    2. Simplify the fraction.
      =118= \frac{1}{18}

    Answer: 118\frac{1}{18}

Medium

  1. Example 4. A fair six-sided dice is rolled. What is the probability of rolling a multiple of 3?

    1. 2 of the 6 numbers fit.
      P=26P = \frac{2}{6}
    2. Simplify the fraction.
      =13= \frac{1}{3}

    Answer: 13\frac{1}{3}

  2. Example 5. A fair six-sided dice is rolled. What is the probability of rolling an even number?

    1. 3 of the 6 numbers fit.
      P=36P = \frac{3}{6}
    2. Simplify the fraction.
      =12= \frac{1}{2}

    Answer: 12\frac{1}{2}

  3. Example 6. A fair six-sided dice is rolled. What is the probability of rolling a number less than 3?

    1. 2 of the 6 numbers fit.
      P=26P = \frac{2}{6}
    2. Simplify the fraction.
      =13= \frac{1}{3}

    Answer: 13\frac{1}{3}

Hard

  1. Example 7. A bag has 4 red and 2 blue counters. A counter is picked, put back, and a second counter is picked. What is the probability that both are red?

    1. Probability of red each time.
      P(red)=46P(\text{red}) = \frac{4}{6}
    2. Multiply for both picks.
      46×46=49\frac{4}{6} \times \frac{4}{6} = \frac{4}{9}

    Answer: 49\frac{4}{9}

  2. Example 8. A bag has 1 red and 2 blue counters. A counter is picked, put back, and a second counter is picked. What is the probability that both are red?

    1. Probability of red each time.
      P(red)=13P(\text{red}) = \frac{1}{3}
    2. Multiply for both picks.
      13×13=19\frac{1}{3} \times \frac{1}{3} = \frac{1}{9}

    Answer: 19\frac{1}{9}

  3. Example 9. A bag has 5 red and 6 blue counters. A counter is picked, put back, and a second counter is picked. What is the probability that both are red?

    1. Probability of red each time.
      P(red)=511P(\text{red}) = \frac{5}{11}
    2. Multiply for both picks.
      511×511=25121\frac{5}{11} \times \frac{5}{11} = \frac{25}{121}

    Answer: 25121\frac{25}{121}

Your turn

Practise with fresh questions of the same kind. You get hints, the full working and instant checking.

Practise this topicProbability Calculator