Unit E: Statistics and Probability

Chapter 2: Probability

Making Predictions Based on Probability

Weather forecasts are educated guesses made by collecting as much data as possible about atmospheric conditions, temperature, humidity, and wind. While the forecasts are not always correct, modern technology and science allow meteorologists to make much better predictions than 50 years ago.


Probability is used to make a prediction or an educated guess. Sometimes predictions are correct and sometimes they are wrong. Probability is used to approximate the number of favourable outcomes in a situation. The formula used to make a prediction is

prediction of favourable outcomes = probability × total number of outcomes

Use the experimental probability whenever possible when making a prediction. If there is no data to calculate the experimental probability, then use the theoretical probability.

Sam has a 20-sided die.




  1. Predict how many times a 14 will appear if the die is rolled 75 times.

  2. Sam rolled the die and recorded her data in the table below.

    Outcome 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 total
    Frequency 4 3 0 4 3 5 2 3 5 7 1 3 6 8 1 5 2 5 2 6 75


    Compare the results of the experiment to the prediction.

  3. If Sam repeated the experiment, how many times would she roll a 14?

  4. If Sam repeated the experiment, is it possible for a 14 to be rolled 75 times?


  1. Step 1: Find the probability of rolling a 14.

    probability = number   of   favourable   outcomes total   number   of   possible   outcomes = number   of   sides   that   show   a   14 number   sides   on   the   die = 1 20 = 0 . 05

    Step 2: Substitute the probability, 0.05, and the number of times rolled, 75, into the formula.

    prediction   of   favourable   outcomes = probability × total   number   of   outcomes = 0 . 05 × 75 = 3 . 75
    Always round the prediction to the nearest whole number.

    A 14 will be rolled approximately four times.

  2. The prediction was that a 14 would be rolled four times. However, when Sam performed the experiment, a 14 appeared eight times.

  3. A prediction is an educated guess but does not guarantee a certain outcome. If the experiment was repeated a second time, a 14 could be rolled anywhere between 0 and 75 times.

  4. It is possible for a 14 to be rolled 75 times; however, it is highly unlikely.
Two dice were rolled 22 times. When the dice added up to 8, the result was recorded. This event occurred 5 times.





  1. What is the probability of rolling a sum of eight on the dice?

  2. Predict how often a sum of eight will appear on the dice if 600 trials are completed.

  1. Find the probability of rolling a sum of eight, using the data given.

    probability = number   of   favourable   outcomes total   number   of   possible   outcomes = number   of   times   the   sum   of   the   dice   is   eight total   number   of   rolls = 5 22 = 0 . 227

    The experimental probability that the sum of eight will be rolled is 0.227.

  2. To calculate how many times a sum of eight is rolled, multiply the probability by the number of rolls.

    prediction   of   favourable   outcomes = probability × total   number   of   outcomes = 0 . 227 × 600 = 136 . 2

    The number of times a sum of eight will be rolled if 600 trials are performed is 136.
Gabriela asked a sample of students to name their favourite type of pizza. The choices were cheese, pepperoni, or Hawaiian.


 



  1. Calculate the theoretical probability that a student's favourite pizza is pepperoni.

  2. Gabriela surveyed some of her classmates and recorded the data in the table below.

    Topping Number of Students
    cheese 4
    pepperoni 22
    Hawaiian 9
    Total 35



    Calculate the experimental probability that a student's favourite pizza is pepperoni.

  3. Gabriela would like to predict the number of students that prefer pepperoni pizza. Should she use the theoretical probability or experimental probability in her calculation?

  4. There are 400 students at Gabriela's school. Predict the number of students who prefer pepperoni pizza.


  1. probability = number   of   favourable   outcomes total   number   of   possible   outcomes = favourite   pizza   is   pepperoni total   choices   of   pizza = 1 3 = 0 . 333



    The theoretical probability is 0.333.


  2. probability = number   of   favourable   outcomes total   number   of   possible   outcomes = number   of   students   who   chose   pepperoni total   number   of   students   in   sample = 22 35 = 0 . 629


    The experimental probability is 0.629.


  3. Each person has their own favourite type of pizza. The theoretical probability would not give an accurate result since each type of pizza is not equally likely. The prediction will be more accurate if the data collected in the survey is used to make the prediction. Therefore, the experimental probability should be used.

  4. Substitute the experimental probability, 0.629, and the number of students, 400, into the formula.

    prediction   of   favourable   outcomes = probability × total   number   of   outcomes = 0 . 629 × 400 = 251 . 6

    There will be approximately 252 students in the school that prefer pepperoni pizza.