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?
boys --- b
girls ---- g
b + g = 20 or g = 20-b
prob( boy is chosen) = b/20
prob(girl is chosen) = g/20
but g/20 = (2/3)(b/20
g/20 = b/30
3g = 2b
3(20-b) = 2b
60 - 3b = 2b
5b = 60
b = 12
so 12 boys and 8 girls
for every 2 girls, there are 3 boys to choose from
2/5 of 20 is 8
8 is right
To determine the number of girls in the debate team, let's assign variables and set up an equation based on the given information.
Let:
G = the number of girls in the debate team
B = the number of boys in the debate team
We know that the probability of choosing a girl (P(girl)) is 2/3 the probability of choosing a boy (P(boy)). Since each member is equally likely to be chosen, we can express this relationship as an equation:
P(girl) = 2/3 * P(boy)
The probability of choosing a girl is G/20 because there are G girls out of a total of 20 members. Similarly, the probability of choosing a boy is B/20.
Substituting these expressions into the equation, we get:
G/20 = 2/3 * (B/20)
Now, let's solve for G:
G/20 = 2B/60
G = (2B * 20) / 60
G = B/3
From the equation, we can see that the number of girls (G) is one-third of the number of boys (B).
Since the problem does not specify the actual values of B, we cannot determine the exact number of girls in the debate team without additional information. However, we can say that the number of boys (B) will always be three times the number of girls (G) in order to satisfy the given conditions.