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?

Guest May 20, 2019

#1**+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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.hectictar May 20, 2019