How much should I pay to play? If your chance of
winning £100 in a game is 0.05, a fair price for playing is 0.05 x £100 = £5 Similarly, if you win £50 for a head and lose £40 for a tail. the fair price would be ½ x £50  ½
x £40 = £5. The
Problems : 1.
What should you pay to play a game where you win £10 for every spot
showing when a die is thrown once? 2. What should you pay to play
a game where you win £10 for every spot showing when two dice are thrown once? 3. This next game is supposed to have been played at St Petersburg:
A coin is
tossed until a head appears. If it
appears on the first toss, you win £1. If it first appears on the
second toss, you win £2. If it
appears for the first time on the third toss, you win £4, and
so on, doubling each time. (a)
What is the probability that you will win exactly £32? That you will win more than £32? That you will win less
than £32? (b)
If the game stops after 10 throws, what would be a fair price to pay? (c) If it is to go on, regardless of
how long the game takes, what would be a fair
price to pay?
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