Banking, Finance & Insurance - ACTUARY

Race to the Top

Primary Middle

Australian Curriculum General Capability: Numeracy

Cooperative Learning Activity

1. Actuaries deal with probability all the time. You are to experience probability in the following game.

In teams, get two 1-6 dice and print off the following Game Board - one per team.

2. Students roll the dice and record an “x” above the sum of the two dice. Students continue rolling, adding, and marking the sums for the duration of the game.

3. The first number to reach the finish line is the winner. Play should continue until the first 3 places are determined (or time runs out).

4. The winning number should now be referred to as the “mode” (most frequently occurring number).

As a team, work out:

• Was this game fair for all of the numbers? (Fair means that all sums had equally likely chances to be rolled.)
• Which sums were impossible?
• Which sums were more likely to be rolled?
• Which sums were less likely to be rolled?

5. Print out the Game Board Sheet again. This time use the following Random Dice generator to see if there is any difference.

6.

Reflection:

Was there a difference? Why?

“Is It Fair?”

Middle Secondary

Australian Curriculum General Capability: Numeracy

Australian Curriculum General Capability: Personal and social capability

Australian Curriculum General Capability: Ethical Understanding

Teacher

  
Objectives: Students will be introduced to:

• the role probability plays in assessing risk
• the concept that groups representing higher risks will pay higher insurance rates

1. One student acting as The Actuary is to write the following statistics on the board:

• For every 1,000 automobiles on the road in the state of "Confusion", there were an estimated 150 accidents for male drivers versus 75 accidents for female drivers.
• Males age 16 to 23 are four times more likely to be involved in an accident than the average male driver.
• Females age 16 to 23 are two times more likely to be involved in an accident than the average female driver.
• Students (high school or university/TAFE) with good grades (GPA 3.0 or higher) have half the number of accidents as those with a lower GPA.
• The average cost of an accident for all drivers is $5,000.

2. The Actuary is to tell the class that, while the figures here are illustrative, insurance rates for teenage boys, particularly those driving expensive/sports cars, are among the highest rates charged any group.

3. As a class discuss why insurance companies charge higher rates for teenage boys and whether or not it is fair.

The Actuary notes that insurers consider probability when setting rates for large numbers of people.

4. As a group, estimate how much each of the following four groups should pay for insurance:

• Youthful males with a low GPA
• Youthful males with a high GPA
• Youthful females with a low GPA
• Youthful females with a high GPA

5. Read the following article [long and comprehensive!] and then investigate how much it would cost for you if you are 17 and using your family car: "Compare Car Insurance"

What was the best car in terms of cost?

The table below illustrates values to demonstrate the cost differences by driver type.

6. From this article how could you improve your chances of reducing car insurance rates?

Discuss this as a class. Answer the question:

Is it fair?
(Source: Adapted from Actuarial Foundation)