a ranch has 7 geese and x ducks.2 animals are selected one after another without replacement. given that the probability that a geese and a duck are seleced is 7/15, and there are more geese than ducks, what is the value of x?
+118703 Number of geese = 7
Number of ducks = x
More geese than ducks so x<7
Probability of a goose and a duck chosen = 2(7x+7×xx+7−1)
I times by 2 because the probability of choosing a duck and then a goose is the same.
2(7x+7×xx+7−1)=7152(7x+7×xx+6)=71514x(x+7)(x+6)=715multiply both sides by 15(x+7)(x+6) to get rid of all the fractions15∗14x=7(x+7)(x+6)30x=x2+13x+420=x2−17x+420=(x−3)(x−14)x=3orx=14butx<7thereforex=3
So there are 3 ducks and 7 geese.
+118703 Number of geese = 7
Number of ducks = x
More geese than ducks so x<7
Probability of a goose and a duck chosen = 2(7x+7×xx+7−1)
I times by 2 because the probability of choosing a duck and then a goose is the same.
2(7x+7×xx+7−1)=7152(7x+7×xx+6)=71514x(x+7)(x+6)=715multiply both sides by 15(x+7)(x+6) to get rid of all the fractions15∗14x=7(x+7)(x+6)30x=x2+13x+420=x2−17x+420=(x−3)(x−14)x=3orx=14butx<7thereforex=3
So there are 3 ducks and 7 geese.
