Exercise 1 Page 691

As discussed in the previous exercise, consider that we randomly draw a number from $1$ to $30.$ The method presented in the exercise attempted to use the complement to find the probability that a number is greater than $4.$ The issue was that the student incorrectly identified the values included in the complement. The student used only the numbers $1,$ $2,$ and $3$ because they only considered numbers strictly less than $4.$ We could have explained this error using a number line. Let's do it! In the number line below, the $\text{left}$ segment represents the numbers considered by the student and the $\text{right}$ segment represents its complement.

Looking at the number line, we can see that the $\text{right}$ segment includes $4$ — it has a closed dot. However, this should not be the case. The actual complement of the set of numbers greater than $4$ is numbers that are less than or equal to $4.$ Let's represent this on a new number line.

We can see that this time the $\text{right}$ segment does not contain the number $4$ — it has an open dot. This number line correctly displays the desired outcomes that should be included in the probability calculations.