Age 16 to 18 Challenge Level:
Risk and reward are fundamental
concepts in probability and chance: the more risky something is,
the more reward you demand for taking part in that
Here are some starting points for discussion or thought about
risk, probability and reward. As you consider each point, try to
validate your points clearly using well reasoned arguments or
equations. Note that there is no 'right' answer to some of these
questions. You might wish to find someone mathematically minded and
debate these questions with him or her.
1. A lottery ticket costs £1, and 45% of the winnings are paid
out in prizes. So, the fair price of a lottery ticket should be
2. A friend invites you to play a game where you roll a die. If a 6
comes up you win a prize of £1. How much would you pay to play
this game a large number of times?
3. The same friend from question 2 adjusts the game so that if you
roll a 6 then you win £1, but if you roll a 1 you have to pay
an additional £1. How much would you pay to play this game 100
4. A raffle is being held. There are 1000 tickets and a single top
prize of £1000. How much would you pay for a ticket?
5. A lottery is being held in which there is a top prize of £X
and 10X tickets are to be sold. For what range of X would you be
prepared to spend £1 on a ticket?
6. Two treatments for a presently untreatable disease are under
development. Treatment A is ambitious: If the treatment is
successfully developed, it would cure all patients with the
disease. This treatment will take 10 years to develop but has
a 50% chance of failing its development. Treatment B is less
ambitious: If the treatment is successfully developed it would cure
50% of patients with the disease. This treatment will also take 10
years to develop, but the programme is 90% likely to end up with a
successful treatment. Which would you back? What data would you
need to make your decision?
7. You buy a house and are offered two mortgage products. The first
will cost you £1000 per month for 20 years, and is guaranteed
to pay off your mortgage at the end of the 20 years. The second
will also cost you £1000 per month for 20 years, but this will
pay off the mortgage and pay you a bonus sum of £50,000 at the
end of the 20 years with a 95% probability. However, there is a 5%
chance that the investment will go sour and you will lose
everything at a random point during the 20 years. Which product
would you pick?
8. A certain physical activity is said to be highly exhilarating,
but comes equipped with a 1 in 10,000 chance of breaking your leg.
Would you take part?
9. Can you think of situations taught in different school subjects
in which a risk is balanced by a reward?
10. Consider the challenge of inventing a way to 'measure' the risk
associated with various physical activities, such as motorbike
riding, walking, smoking or running whilst holding scissors. Once
you have a system, why not try plotting these on a