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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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Hints/Tips short amendment | Comment 8 of 14 |

The constraint ( b<2k, g<2k) was unnecessary and stupid, introducing unnecessary noises.

The only valid restriction should be (b+g)<2k - i.e. not enough tickets to please all the students.

However, nothing prevented solving the sample (not restricted) by the simplest way:

P(gs get 5 tkts)=C(14,5)*C(6,3)/C(20,8)

P(gs get 6  tkts)=C(14,6)*C(6,2)/C(20,8)

P(gs get 7  tkts)=C(14,7)*C(6,1)/C(20,8)

P(gs get 8  tkts)=C(14,8)*C(6,0)/C(20,8)

P(gs get over 4 tkts)=sum of the results above=

  = .31785 +  .35759 + .16347 + . 02384 =

I leave it to you to generalize for b, g, 2k;  such that b+g<2k .

  Rem: a consistent typo corrected following Charlie's remark.

Edited on October 14, 2014, 9:52 am
  Posted by Ady TZIDON on 2014-10-11 02:00:08

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