Respuesta :
Answer:
The probability that no more than 1 person is not employed is 0.5077.
Step-by-step explanation:
Let's denote the events as:
E = a person is employed
M = a person is male
F = a person is a female.
Given:
P (E | M) = 0.80
P (E | F) = 0.60
P (F) = 0.55
P (M) = 1 - P (F) = 1 - 0.55 = 0.45
Compute the probability that a randomly selected person is employed as follows
P (E) = P (E | M) × P (M) + P (E | F) × P (F)
[tex]=(0.80\times0.45)+(0.60\times0.55)\\=0.69[/tex]
Then the probability that a randomly selected person is not employed is,
P (E') = 1 - P (E) = 1 - 0.69 = 0.31
Now let's assume X = number of employees that are not employed.
The sample selected is of size, n = 5.
Then the random variable [tex]X\sim Bin(n=5, p=0.31)[/tex]
The probability function of Binomial distribution is:
[tex]P(X=x)={n\choose x}p^{x}(1-p)^{n-x}[/tex]
Compute the probability that no more than 1 person is not employed as follows:
P (X ≤ 1) = P (X = 0) - P (X = 1)
[tex]={5\choose 0}(0.31)^{0}(1-0.31)^{5-0}+{5\choose 1}(0.31)^{1}(1-0.31)^{5-1}\\=0.1564-0.3513\\=0.5077[/tex]
Thus, the probability that no more than 1 person is not employed is 0.5077.
