Respuesta :
Answer:
i) [tex]P(X=2)=(20C2)(0.25)^2 (1-0.25)^{20-2}=0.0669[/tex]
ii) [tex]P(X=0)=(20C0)(0.25)^0 (1-0.25)^{20-0}=0.00317[/tex]
[tex]P(X=1)=(20C1)(0.25)^1 (1-0.25)^{20-1}=0.0211[/tex]
[tex]P(X=2)=(20C2)(0.25)^2 (1-0.25)^{20-2}=0.0669[/tex]
And replacing we got:
[tex] P(X \geq 3) = 1- [0.00317+0.0211+0.0669]= 0.90883[/tex]
iii) [tex]P(X <2)= 0.00317+ 0.0211= 0.02427[/tex]
Step-by-step explanation:
Let X the random variable of interest "number of inhabitants of a community favour a political party', on this case we now that:
[tex]X \sim Binom(n=20, p=0.25)[/tex]
The probability mass function for the Binomial distribution is given as:
[tex]P(X)=(nCx)(p)^x (1-p)^{n-x}[/tex]
Where (nCx) means combinatory and it's given by this formula:
[tex]nCx=\frac{n!}{(n-x)! x!}[/tex]
Part i
We want this probability:
[tex]P(X=2)=(20C2)(0.25)^2 (1-0.25)^{20-2}=0.0669[/tex]
Part ii
We want this probability:
[tex]P(X\geq 3)[/tex]
And we can use the complement rule and we have:
[tex]P(X\geq 3) = 1-P(X<3)= 1-P(X \leq 2) =1- [P(X=0) +P(X=1) +P(X=2)][/tex]
And if we find the individual probabilites we got:
[tex]P(X=0)=(20C0)(0.25)^0 (1-0.25)^{20-0}=0.00317[/tex]
[tex]P(X=1)=(20C1)(0.25)^1 (1-0.25)^{20-1}=0.0211[/tex]
[tex]P(X=2)=(20C2)(0.25)^2 (1-0.25)^{20-2}=0.0669[/tex]
And replacing we got:
[tex] P(X \geq 3) = 1- [0.00317+0.0211+0.0669]= 0.90883[/tex]
Part iii
We want this probability:
[tex] P(X <2)= P(X=0) +P(X=1)[/tex]
And replacing we got:
[tex]P(X <2)= 0.00317+ 0.0211= 0.02427[/tex]
