I have a nice (?) probability question for you to take away on holiday, or
give to anyone you wish to keep quiet for a while.
The question is "practical", as I want the answer for a "Prime Tombola" to
be run at a Maths FunFair in York next October.
The rules of Prime Tombola (version 1) are this:
* for 1 pound you buy THREE tickets
* each ticket has a 2-digit number from 00 to 99
* you can win a prize in one of three ways:
a. if you have a 2-digit prime up to 100
b. if you can make a 4-digit prime (from 100 to 10000)
c. if you can make a 6-ticket prime (from 10000 to 1,000,000)
What, please are the probabilities of a-c?
What is the probability that NONE of these events occurs?
And what value should I put on prizes for a-c in order to encourage people
to buy while remaining solvent?
I can offer a free overnight in York to the first person producing an
adequate solution; if anyone wants a list of prime numbers up to 1 million,
I can provide this too.
Thanks you for your attention - and have a nice summer!
JOHN BIBBY
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