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Picking numbers (Posted on 2015-07-17) Difficulty: 3 of 5
Bernardo randomly picks 3 distinct numbers from the set (1; 2; 3; 4; 5; 6; 7; 8; 9) and arranges them in descending order to form a 3-digit number.
Silvia randomly picks 3 distinct numbers from the set (1; 2; 3; 4; 5; 6; 7; 8) and also arranges them in descending order to form a 3-digit number.

What is the probability that Bernardo's number is larger than Silvia's number?
Source: AMO

See The Solution Submitted by Ady TZIDON    
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re: Analytical Solution (spoiler) | Comment 2 of 7 |
(In reply to Analytical Solution (spoiler) by Steve Herman)

111/168 does agree with my calculations and reduces to 37/56.


However, I don't think that Bernardo would have exactly 2/3 probability if they picked new numbers in the event of a tie. Silvia's probability of getting the higher number immediately is 55/168 (i.e., (2/3)*(55/56)/2), so if we discount the ties and continue choosing, Bernardo has a 111/(111+55) ~= .668674698795181 probability.

Edited on July 17, 2015, 3:18 pm
  Posted by Charlie on 2015-07-17 15:08:32

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