A gambler bets half the money in his pocket on the toss of a coin,
winning an equal amount for a head and losing his money if the
result is a tail. After 2n plays he has won exactly n times. Has he
more money than he started with?
You have two bags, four red balls and four white balls. You must
put all the balls in the bags although you are allowed to have one
bag empty. How should you distribute the balls between the two bags
so as to make the probability of choosing a red ball as small as
possible and what will the probability be in that case?
To win on a scratch card you have to uncover three numbers that add
up to more than fifteen. What is the probability of winning a
prize?
Coin Lines
Age 14 to 16 Challenge Level:
A coin is randomly tossed onto a set of parallel lines. If the
line separation matches the diameter of the coin, what is the
chance that the coin touches a line?
And what if the line separation is different ? Double ? Half
?
If the lines become concentric circles and the gap between the
lines doubles, what is the chance now that the coin touches a
line?
An answer might be guessed at but
the problem is really about justifying that answer.
Do you have a way of visualising it
and could you convince a friend?
If you succeed with that it should be
an easy next step to generalise for a coin of any size.