Exercise 113 Page 65

Practice makes perfect

a Probability is calculated by dividing the number of favorable outcomes by the number of possible outcomes.

P=Number of favorable outcomes/Number of possible outcomes To investigate the number of favorable and possible outcomes we should first illustrate the shape bucket of Sandy and Robert.

Notice that Sandy has a total of 4 shapes in her bucket and Robert has a total of 5 shapes. To identify the number of favorable outcomes, we have to single out the quadrilaterals in the buckets. This is a shape with four vertices.

As we can see, Sandy has 2 quadrilaterals in her bucket and Robert has 3. Now we can calculate the probability of Sandy and Robert selecting a quadrilateral. Sandy:& 2/4=50 % [0.8em] Robert:& 3/5=60 % Robert has a greater probability of picking a quadrilateral.

b An equilateral shape has sides which are all equally long. This is true for all of Sandy's shapes and none of Robert's shapes.

Sandy has a 100 % probability of picking a shape that is equilateral while Robert has a 0 % chance of picking an equilateral shape. Therefore, Sandy has a greater probability of selecting an equilateral shape.

c Note that "at least two sides" can be expressed as "at least a pair of sides". In Sandy's bucket, the square, rhombus, and a regular hexagon all have at least one pair of sides that are parallel. In Robert's bucket, we have three shapes with at least one pair of sides that are equal.

Now we can calculate the probability of Sandy selecting a shape with at least two sides that are parallel and of Robert selecting a shape with at least two sides that are equal. Sandy:& 3/4=75 % [0.8em] Robert:& 3/5=60 % Sandy has a greater probability of selecting a shape with at least two sides that are parallel.

Subchapter links

1.3.1 Attributes and Characteristics of Shapes p.64-65

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1.3.2 More Characteristics of Shapes p.68-69

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Exercise 113 Page 65

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