Given that b<2k and g<2k, what is the probability that within the group of theatregoers there will be more girls than boys?
No Solution Yet  Submitted by Ady TZIDON 
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re(2): Solution or partial solution ... clarification 

For the derivation of the above, to take the case of the girls' receiving 5 tickets:
For one particular combination of 5girl ticket distribution (say gbggbgbg, but the explanation goes better with gggggbbb), there's 14/20 prob. that a girl will actually get that first ticket we'd want to go to a girl, and 13/19 for the second thats hoped to go to a girl, and so on down to 10/16 for the fifth. Then there are only 6 out of the remaining 15 students that are boys; then 5 out of 14 and 4 out of 13. That reaches the end of the 8 tickets to be distributed. Note that we've only covered gggggbbb. There are actually C(8,5) cases where 5 girls and 3 boys get tickets, each with identical probability, and so we multiply by that value.
Edited on October 10, 2014, 7:54 am
Posted by Charlie on 20141009 09:56:20 