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One member of the debate team is going to be chosen President. Each member is equally likely to be chosen. The probability that a girl is chosen is 2/3 the probability that a boy is chosen. If the debate team has 20 people, how many girls are there?

 May 20, 2019
 #1
avatar+8756 
+3

Let the number of girls  =  g

Let the number of boys  =  b

 

b + g  =  20

b  =  20 - g

 

probability that a girl is chosen  =  \(\frac23\)( probability that a boy is chosen )

 

\(\frac{g}{20}\,=\,\frac23(\frac{b}{20})\\~\\ \frac{g}{20}\,=\,\frac23(\frac{20-g}{20})\\~\\ g\,=\,\frac23(20-g)\\~\\ \frac32g\,=\,20-g\\~\\ \frac32g+g\,=\,20\\~\\ \frac52g\,=\,20\\~\\ g\,=\,8\)

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 May 20, 2019
edited by hectictar  May 20, 2019
edited by hectictar  May 20, 2019
 #2
avatar+1538 
+3

Good job Hectitar! I was stumped and now I know how to do this!

CalculatorUser  May 20, 2019
 #3
avatar+8756 
+2

Thanks! I've learned a thing or two from your answers too! laugh

hectictar  May 20, 2019

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