Learn Mathematics with Free Lessons & Tips

Classes explore different scenarios using manipulatives to learn about the difference between independent and dependent probability. Learners experiment with colored chips to model the two types of probabilities. To test their understanding, individuals sort independent and dependent probabilities into like groups.

Real Life Context The following examples could be used to explore real life contexts.

Looking at statistics from the Census, questions like:

• How long will I live?

• Will I get married?

• How many children will I have? These questions can be answered with some degree of certainty based on population statistics. Life assurance companies work out how much to charge for their premiums based on tables of life expectancy. Why are some premiums cheaper than others?

The following examples could be used to explore misconceptions:

• What is the most difficult number to get when throwing a fair die?

• Random events should have outcomes which appear random; for example, in the lotto theory tells us that any of the six numbers is equally likely to turn up, yet more people choose randomly spaced numbers than numbers which form a pattern like 1,2,3,4,5,6 etc.

• The likelihood of 2 consecutive numbers appearing in any Lotto draw (which is > 50%) could easily be investigated by reference to a number of recent draws.

To divide a line segment of 7.6 cm into two parts in the ratio 5:8, the segment is divided into a total of 5+8=13 parts.

The length of each part is 7.6 cm/13 ≈0.5846cm

• The length of the first part (5 parts) is 5×7.6 cm/13 ≈2.923cm
• The length of the second part (8 parts) is 8×7.6 cm/13 ≈4.677cm

Verifying the Sum:

2.923 cm+4.677 cm≈7.6 cm

I'll provide a step-by-step guide on how you can draw these triangles using basic geometry tools:

• Ruler
• Compass
• Pencil
• Protractor (optional for verifying angles)

First Triangle (sides 5cm, 6cm, 7cm) Construction:

1. Draw the Base (5 cm):

   • Draw a horizontal line segment AB of length 5 cm.

2. Draw an Arc (6 cm):

   • Place the compass at point A.
   • Measure 6 cm on the compass.
   • Draw an arc above the line segment AB.

3. Draw an Arc (7 cm):

   • Place the compass at point BBB.
   • Measure 7 cm on the compass.
   • Draw another arc intersecting the first arc.

4.  Mark the Intersection (Point C):

   • Label the intersection point of the arcs as C.

5. Complete the Triangle:

   • Draw line segments AC and BC to complete the triangle ABC.

Second Triangle (sides 4/5th of Frist Triangle) Construction:

1. Calculate the Scaled Sides: The sides of the scaled triangle are 4/5 of the corresponding sides of the first triangle.

• 4/5×5 cm=4cm
• 4/5×6 cm=4.8cm
• 4/5×7 cm=5.6 cm

2. Measure and Draw the Scaled Sides:

1. Draw the Base (4 cm):
   Draw a horizontal line segment DE of length 4 cm.

2. Draw an Arc (4.8 cm):

   • Place the compass at point D.
   • Measure 4.8 cm on the compass.
   • Draw an arc above the line segment DE.

3. Draw an Arc (5.6 cm):

   • Place the compass at point E.
   • Measure 5.6 cm on the compass.
   • Draw another arc intersecting the first arc.

4. Mark the Intersection (Point F):

   • Label the intersection point of the arcs as F.

5. Complete the Triangle:

   • Draw line segments DF and EF to complete the triangle DEF.

154/3 cm²

^{EXPLANATION:-}

Minute hand complete full circle in 1 hour.

To find the mean of the 32 numbers, we can use the concept of weighted averages.

Given:

1. The mean of 10 of the numbers is 15.
2. The mean of 20 of the numbers is 11.
3. The last two numbers are 10.

Let's denote: