Respuesta :
Answer:
[tex] P(X\geq 2)=1- P(X<2)= 1-[P(X=0) +P(X=1)][/tex]
And using the probability mass function we can find the individual probabilities:
[tex]P(X=0)=(8C0)(0.18)^0 (1-0.18)^{8-0}=0.2044[/tex]
[tex]P(X=1)=(8C1)(0.18)^1 (1-0.18)^{0-1}=0.3590[/tex]
And replacing we got:
[tex] P(X\geq 2)=1 -[0.2044 +0.3590]= 0.4366[/tex]
Then the probability that at least 2 disapprove of daily pot smoking is 0.4366
Step-by-step explanation:
Let X the random variable of interest "number of seniors who disapprove of daily smoking ", on this case we now that:
[tex]X \sim Binom(n=8, p=0.18)[/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]
And we want to find this probability:
[tex] P(X\geq 2)=1- P(X<2)= 1-[P(X=0) +P(X=1)][/tex]
And using the probability mass function we can find the individual probabilities:
[tex]P(X=0)=(8C0)(0.18)^0 (1-0.18)^{8-0}=0.2044[/tex]
[tex]P(X=1)=(8C1)(0.18)^1 (1-0.18)^{0-1}=0.3590[/tex]
And replacing we got:
[tex] P(X\geq 2)=1 -[0.2044 +0.3590]= 0.4366[/tex]
Then the probability that at least 2 disapprove of daily pot smoking is 0.4366
