A typical London cyclist might expect to earn £40k a year. This is reduced to £20k for one year following a serious inju

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A typical London cyclist might expect to earn £40k a year. This
is reduced to £20k for one year following a serious injury. The
annual probability of a serious injury is 35%.
(a) What is the expected annual income of a cyclist in London?
[5 Marks] (b) A group of risk-adverse London cyclists agree to form
a charity providing insurance. Those paying a fixed annual premium
will receive £20,000 in the event of an accident. What is the
“fair” (zero-profit) premium for this insurance policy? Show your
work.
(c) Research has found that wearing a yellow head-protector can
reduce the annual risk of injury to zero. Show in a large clearly
labelled graph the maximum price that a risk-adverse cyclist would
pay for a head-protector. Note: the answer given does not need to
be precise but must be consistent with your graph.