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Big Ideas Math Geometry, 2014

BI

Big Ideas Math Geometry, 2014 View details

What Did You Learn?

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Exercise 1 Page 691

On the number line, draw a line segment that includes the numbers greater than 4.

See solution.

Practice makes perfect

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. P( >4 ) = 1-P( < 4 ) * P( >4 ) = 1-P( ≤ 4 ) ✓

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 left segment represents the numbers considered by the student and the right segment represents its complement.

Looking at the number line, we can see that the 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 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.

Subchapter links

Mathematical Practices p.691-713