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?
+9466 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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