Question

A school debate team has 4 girls and 6 boys. A total of 3 of the team members will be chosen to participate in the district debate. What is the probability that 3 girls and no boys will be selected?

Answer 1

The probability is out of ten so the answer would be 2/5

Answer 2

The probability is 0.064

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=(4)/(10)=(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)=(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