32 members of our social group use the weekly results of our national lotto draw for our competition. Each person selects a set of 3 numbers from just one of the coloured grids of the map shown below, such that they are all in a row (e.g. 31, 32 and 33) or in a column (e.g. 23, 29 and 35) or diagonally (e.g. 06, 11 and 16):

	01	02	03		04	05	06
	07	08	09		10	11	12
	13	14	15		16	17	18
	19	20	21		22	23	24
	25	26	27		28	29	30
	31	32	33		34	35	36

Our national lotto draws, each week, 5 numbers from the set of 36 numbers, and we permanently mark these 5 numbers in our map. The winner in our competition will be the person who firstly has his 3 numbers marked.

What is the probability that our competition:
a) ends in the first week?
b) ends in the second week?
c) ends in the third week?

And the most important:
d) What is the expected number of weeks for us to have a winner?

(In reply to a minor mistake... by pcbouhid)

I have given levik appropriate information and asked him to make a correction. 

Apologies for that compilation.

Posted by brianjn on 2009-06-12 23:46:34