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A personal lotto game (Posted on 2009-06-12) Difficulty: 3 of 5
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?

See The Solution Submitted by pcbouhid    
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Comments: ( You must be logged in to post comments.)
  Subject Author Date
re(2): a minor mistake...pcbouhid2009-06-13 00:02:36
re: a minor mistake...brianjn2009-06-12 23:46:34
Some ThoughtssimulationCharlie2009-06-12 15:57:05
a minor mistake...pcbouhid2009-06-12 14:02:11
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