Probability of picking fish from a tank

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The discussion revolves around calculating the probability of selecting at least half male guppies from a tank containing 12 males and 12 females when 15 fish are randomly chosen. The initial approach involves calculating the probabilities for selecting 6 to 12 males, which can be cumbersome. A more efficient method suggested is to use the complement probability by calculating the chances of selecting fewer than half males, specifically 0, 1, or 2 males, which simplifies the process. Participants agree that this approach reduces the number of calculations needed. Overall, the discussion highlights the importance of using complementary probabilities in solving such problems.
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Homework Statement



a fish tank contains 12 male and 12 female guppies what is the probability that at least half of male will be selected if 15 fish are randomly selected and removed from the tank??

Homework Equations





The Attempt at a Solution


i am tried to find the probability as following :
P(at least 6)=P(6)+P(7)+P(8)+P(9)+P(10)+P(11)+P(12)
=(12c6)(12c6)/(24c15) + (12c7)(12c5)/(24c15)+...+(12c12)(12c3)/(24c15)
it seems to be a very long solution is there any way to solve it using the distribution function
 
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ecesiu said:

Homework Statement



a fish tank contains 12 male and 12 female guppies what is the probability that at least half of male will be selected if 15 fish are randomly selected and removed from the tank??

Homework Equations





The Attempt at a Solution


i am tried to find the probability as following :
P(at least 6)=P(6)+P(7)+P(8)+P(9)+P(10)+P(11)+P(12)
=(12c6)(12c6)/(24c15) + (12c7)(12c5)/(24c15)+...+(12c12)(12c3)/(24c15)
it seems to be a very long solution is there any way to solve it using the distribution function

Some problems just need a long solution; this is one of those. You ARE using the distribution function---that is exactly how you would compute it!

RGV
 
Also you might want to calculate the probability that LESS than half are chosen, since
P(0,1,2) are all zero. So you only need to calculate three values instead of 7.
 
thank you very much Ray Vickson , hgfalling it really nice idea to take the complement thanks
 

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