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?
The probability that a girl is chosen is 2/3 the probability that a boy is chosen.
This means that if there are x boys, there are a total of 2/3 x girls.
The total amount of kids in the class is 2/3x + 1x = 5/3x.
This is equal to 20.
Therefore, there are \(12\cdot\frac23=8\) girls.
We can verify this. The class has 20 people, 8 girls and 12 boys.
The probabilty a girl is chosen is 8/20 and boy is 12/20.
8/20 is also 2/3 of 12/20, so our answer is correct.
I hope this helped,