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Draw and go (Posted on 2014-10-08) Difficulty: 3 of 5
A class, consisting of g girls and b boys receieved 2k promotional theatre tickets.
Given that b<2k and g<2k, what is the probability that within the group of theatre-goers there will be more girls than boys?

No Solution Yet Submitted by Ady TZIDON    
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Some Thoughts re: short amendment | Comment 10 of 14 |
"The only valid restriction should be (b+g)<2k - i.e. not enough tickets to please all the students."

For there not to be enough tickets to please all the students, II believe the inequality should be (b+g)>2k, as (b+g) is the size of the group and 2k is the number of promotional theatre tickets. If the group size is less than the number of tickets, there would be excess tickets and each of the group would be able to be a theatre-goer.

If I did it right, a formula for the general case can be the following:
SUMMATION (t = 1 to k) :
g!*b!*(b+g-2k)!*(2k)!*(g-k-t)! / ((b+g)!*(b+g-k-t)!*((k+t)!*(k-t)!)^2)

Edited on October 11, 2014, 11:39 pm
  Posted by Dej Mar on 2014-10-11 22:55:11

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