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# which are the real odds? frequency matters? how?

Fri 2 Sep, 2011 12:01 pm
Problem 1 data:

A lottery of 10 numbers (0...9) w/o repetition drawing sets of 6.

Statistical data:

A. The statistical probability of a lottery drawing 6 distinct numbers is 19.66%
E.g.: 123456

B. The statistical probability of a lottery drawing 4 distinct numbers and a repeated pair is 49.95%
E.g.: 123455

1. The player always playing 6 distinct numbers has
C(6,6)*C(10-6,0)/C(10,6)=1/210 probability
to match case A. or lottery's 6 distinct numbers and win 1st prize
E.g.:
lottery:123456
player :123456

2. The player always playing 4 distinct numbers and a repeated pair has
C(5,5)C(10-5,0)/C(10,5)=1/252 + (1/252)*1/5=6/1260=1/210 probability
to match case B. or lottery's drawing 4 distinct numbers and a repeated pair and win 1st prize
E.g.:
lottery:123455
player :123455

Which of the following probabilities and statements are correct:

I. Player has (1/210)/(1/210), or same chance whatever he chooses, 1. or 2.

or

II. Player can win 1st prize:
19.66% of the time with 1/210 probability playing 1.
49.95% of the time with 1/210 probability playing 2.

so, the player has 49.95/19.66=x2.54 better chance playing 2., or 4 distinct numbers and a repeated pair against the lottery 4 distinct numbers and a repeated pair.
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