Respuesta :
Answer:
[tex] P(X>1)= 1-P(X \leq 1)= 1- [P(X=0) +P(X=1)][/tex]
And if we use the probability mass function we got:
[tex]P(X=0)=(4C0)(0.6)^0 (1-0.6)^{4-0}=0.0256[/tex]
[tex]P(X=1)=(4C1)(0.6)^1 (1-0.6)^{4-1}=0.1536[/tex]
And replacing we got:
[tex] P(X>1) =1- [0.0256 +0.1536]= 0.8208[/tex]
Step-by-step explanation:
Let X the random variable of interest, on this case we now that:
[tex]X \sim Binom(n=4, p=0.6)[/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]
We want to find the following probability:
[tex] P(X >1)[/tex]
And for this case we can use the complement rule and we got:
[tex] P(X>1)= 1-P(X \leq 1)= 1- [P(X=0) +P(X=1)][/tex]
And if we use the probability mass function we got:
[tex]P(X=0)=(4C0)(0.6)^0 (1-0.6)^{4-0}=0.0256[/tex]
[tex]P(X=1)=(4C1)(0.6)^1 (1-0.6)^{4-1}=0.1536[/tex]
And replacing we got:
[tex] P(X>1) =1- [0.0256 +0.1536]= 0.8208[/tex]
