Respuesta :
Answer:
The probability that exactly two of the four live in their own household and are income-qualified is = .0975
Step-by-step explanation:
Given -
Approximately 85% of persons age 70 to 84 live in their own household and are income-qualified for home purchases.
Probability of sucess ( p ) = 85% =.85
Probability of failure ( q ) = 1 - .85 =.15
n = 4
From combination of n events taking r sucess we use binomial distribution
[tex]P(X = r) = \binom{n}{r}p^{r}q^{n-r}[/tex]
where , r = 2
the probability that exactly two of the four live in their own household and are income-qualified is =
[tex]P(X = 2) = \binom{4}{2}0.85^{2}0.15^{4 - 2}[/tex]
= [tex]\frac{4!}{(2!)(2!)} \times 0.7225 \times .0225[/tex]
= [tex]6 \times 0.7225 \times .0225[/tex]
= .0975
The correct option is C ([tex]0.0975[/tex]).
Probability:
Probability is a measure of the likelihood of an event to occur. Many events cannot be predicted with total certainty. We can predict only the chance of an event to occur, i.e., how likely they are to happen, using it. Probability can range in from 0 to 1, where 0 means the event to be an impossible one and 1 indicates a certain event.
Number of persons randomly selected from the population [tex](n)=4[/tex]
Probability of income-qualified persons[tex]=0.85[/tex]
By using the binomial distribution.
[tex]P(X)=_{}^{n}\textrm{C}_{x}[/tex]
[tex]P(2)=_{}^{4}\textrm{C}_{_{2}} \times(0.85)^{2} \times(0.15)^{4-2}[/tex]
[tex]=6\times(0.85)^{2} \times(0.15)^{2}[/tex]
[tex]P(2)=0.0975[/tex]
So, the probability of two of the four income-qualified living in their own household person is [tex]0.0975[/tex].
Learn more about the topic Probability: https://brainly.com/question/25773035
