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# Probability help needed thx

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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?

math statistics
Sep 2, 2014

#1
+94976
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Number of geese = 7

Number of ducks = x

More geese than ducks so  x<7

Probability of a goose and a duck chosen =       $$2(\frac{7}{x+7}\times \frac{x}{x+7-1})$$

I times by 2 because the probability of choosing a duck and then a goose is the same.

$$\\2(\frac{7}{x+7}\times \frac{x}{x+7-1})=\frac{7}{15}\\\\ 2(\frac{7}{x+7}\times \frac{x}{x+6})=\frac{7}{15}\\\\ \frac{14x}{(x+7)(x+6)}=\frac{7}{15}\\\\ \mbox{multiply both sides by 15(x+7)(x+6) to get rid of all the fractions}\\\\ 15*14x=7(x+7)(x+6)\\\\ 30x=x^2+13x+42\\\\ 0=x^2-17x+42\\\\ 0=(x-3)(x-14)\\\\ x=3\; or\; x=14\\ but\; x<7 \;therefore\\ x=3$$

So there are 3 ducks and 7 geese.

Sep 2, 2014

#1
+94976
+10

Number of geese = 7

Number of ducks = x

More geese than ducks so  x<7

Probability of a goose and a duck chosen =       $$2(\frac{7}{x+7}\times \frac{x}{x+7-1})$$

I times by 2 because the probability of choosing a duck and then a goose is the same.

$$\\2(\frac{7}{x+7}\times \frac{x}{x+7-1})=\frac{7}{15}\\\\ 2(\frac{7}{x+7}\times \frac{x}{x+6})=\frac{7}{15}\\\\ \frac{14x}{(x+7)(x+6)}=\frac{7}{15}\\\\ \mbox{multiply both sides by 15(x+7)(x+6) to get rid of all the fractions}\\\\ 15*14x=7(x+7)(x+6)\\\\ 30x=x^2+13x+42\\\\ 0=x^2-17x+42\\\\ 0=(x-3)(x-14)\\\\ x=3\; or\; x=14\\ but\; x<7 \;therefore\\ x=3$$

So there are 3 ducks and 7 geese.

Melody Sep 2, 2014