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 3digit 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 3digit number.
What is the probability that Bernardo's number is larger than
Silvia's number?
Source: AMO
(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 20150717 15:08:32 