Answer:
The probability is 0.064
Step-by-step explanation:
We know that the school debate team has 4 girls and 6 boys. There are 4 girls in a total of 10 children. Therefore, \(p=\frac{4}{10}=\frac{2}{5}=0.4\)
is the probability of a randomly selected child is girl.
Now, the experiment of randomly select children that we suppose independent and in which we also suppose that every child is a boy or a girl (two possibilities) is called a Bernoulli experiment. The random variable X : ''The randomly selected child is girl'' is a Binomial random variable.
X ~ (n,p)
Where ''n'' is the number of Bernoulli experiment that we make (In this case n = 3 because we choose 3 children of the team members).
\(p=0.4\) because it is the probability of randomly select a girl of the team members.
The probability function for X is :
\(P(X=x)=(nCx).p^{x}.(1-p)^{n-x}\)
Where P(X=x) is the probability of the random variable X to assume the value x
p is called the success probability (0.4 in this case)
(nCx) is the combinatorial number define as
\((nCx)=\frac{n!}{x!(n-x)!}\)
We are looking for \(P(X=3)\) when n = 3 ⇒
\(P(X=3)=(3C3).(0.4)^{3}.(1-0.4)^{3-3}=0.4^{3}=0.064\)
We found out that if a total of 3 of the team members will be chosen (If in the team are 4 girls and 6 boys) the probability that this 3 members chosen being girls is 0.064
