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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?

rohitaop  May 31, 2018
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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. 

 

\(\frac53x=20\Rightarrow{x}=12\)

 

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,

 

Gavin

GYanggg  Jun 1, 2018

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