Let us denote by S the set of 6 integers (their inclusive range being 1 to 37) drawn at random in a weekly lottery.

Given S_ord= (m₁, m₂ ,m₃ ,m₄, m₅, m₆ ) , where the said integers are placed in increasing order, please answer the following questions:

a) What is the expected value of m₁?
b) What is the expected value of m₆?
c) If your "guess set" consists of 6 distinct integers, chosen randomly within the defined range, what is the expected quantity of numbers in this set that match the drawing's results?

Please resolve analytically and then compare your answers with the results of a simulation, based on at least 100,000 independent drawings.

(In reply to reconcider c by Ady TZIDON)

"c totally wrong -is it logical that 97% of random choices coincide with an  unrelated drawing?"

That's not what's being said. What's being said is that there's a

35061/110704 ~=  0.3167094233270703858 probability that none of the numbers match
24273/55352  ~=  0.4385207399913282265 probability that one of the numbers match
22475/110704 ~=  0.2030188611070964011 probability that two of the numbers match
22475/581196 ~=  0.0386702592584945525 probability that three of the numbers match
2325/774928 ~=   0.0030002787355728532 probability that four of the numbers match
31/387464  ~=    0.0000800074329486094 probability that five of the numbers match
1/2324784   ~=   0.000000430147488971 probability that six of the numbers match.

So the mean number of matches is 36/37: less than one of the six tried.

Each number above, such as "one of the numbers match", refers to exactly that number, rather than at least that number.

Edited on March 29, 2013, 9:10 am

Posted by Charlie on 2013-03-29 09:07:22