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artcher [175]
3 years ago
11

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?

Mathematics
1 answer:
inessss [21]3 years ago
7 0
Let
x-------> <span>the probability that a boy is chosen
B------> </span>number of boys in the debate team
G------> number of girls in the debate team<span>

we know that
B+G=20-----> G=20-B-----> equation 1
</span>probability that a boy is chosen=number of boys in the debate team/total of people
so
x=B/20-------> equation 2

t<span>he probability that a girl is chosen is 2/3 the probability that a boy is chosen
</span>probability that a girl is chosen=(2/3)*x
probability that a girl is chosen=G/20
(2/3)*x=G/20-----> equation 3
substitute equation 1 in equation 3
(2/3)*x=[20-B]/20----> equation 4

resolve the equations system
x=B/20
(2/3)*x=[20-B]/20

using a graph tool
see the attached figure
the solution is
x=0.6
B=12
G=20-12-----> G=8

number of boys in the debate team is 12
number of girls in the debate team is 8
the probability that a boy is chosen is 0.6 ----> 60%
the probability that a girl is chosen is 0.6*(2/3)----> 0.4---> 40%

the answer is
number of girls in the debate team is 8

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