Question

1. war veterans approximately 11% of the civilian popu - lation are veterans. choose 5 civilians at random. what is the probability that none are veterans? what is the prob - ability that at least 1 is a veteran?

Explanation:

Step1: Calculate the probability that a single civilian is not a veteran

The probability that a civilian is a veteran is \(p = 0.11\). So the probability that a civilian is not a veteran is \(q=1 - p=1 - 0.11 = 0.89\)

Step2: Use the binomial probability formula for \(n = 5\) and \(k = 0\) (for no - veterans)

The binomial probability formula is \(P(X=k)=C(n,k)\times p^{k}\times q^{n - k}\), where \(C(n,k)=\frac{n!}{k!(n - k)!}\). When \(n = 5\), \(k = 0\), \(p = 0.11\), and \(q = 0.89\)

$$
LATEXBLOCK0
$$

$$P(X = 0)\approx0.559 $$

Step3: Calculate the probability that at least 1 is a veteran

The probability that at least 1 is a veteran is \(P(X\geq1)\). We know that \(P(X\geq1)=1 - P(X = 0)\)
Since \(P(X = 0)\approx0.559\), then \(P(X\geq1)=1 - 0.559 = 0.441\)

Answer:

The probability that none are veterans is approximately \(0.559\). The probability that at least 1 is a veteran is approximately \(0.441\)