# Probability of picking fish from a tank

## 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??

## 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

Related Calculus and Beyond Homework Help News on Phys.org
Ray Vickson
Homework Helper
Dearly Missed

## 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??

## 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