Respuesta :
Answer:
The probability that all five of them have a landline is 20.73%.
The probability that at least one of them does not have a landline 79.27%.
The probability that at least one of them does have a landline is 99.86%.
Step-by-step explanation:
Consider the provided information.
A recent study conducted by a health statistics center found that 27​% of households in a certain country had no landline service.
let p is the probability that they have land line p=0.73
let q is the probability that they have no land line: q=0.27
(a) What is the probability that all five of them have a landline?
[tex]P(X=x)=^n{C_{x}}p^xq^{n-x}[/tex]
[tex]P(X=5)=^5{C_{5}}(0.73)^5(0.27)^{5-5}[/tex]
[tex]P(X=5)=0.2073071593[/tex]
The probability that all five of them have a landline is 20.73%
(b) What is the probability that at least one of them does not have a landline?
P(at least one no landline) = 1-P(All have landline)
P(at least one no landline) = 1-0.2073
P(at least one no landline) = 0.7927
The probability that at least one of them does not have a landline 79.27%.
(c) What is the probability that at least one of them does have a landline?
P(at least one have landline) = 1-P(no one have landline)
P(at least one have landline) = [tex]1-0.27^5[/tex]
P(at least one have landline) = [tex]0.9986[/tex]
The probability that at least one of them does have a landline is 99.86%.
