In a large population, 69% of the people have been vaccinated. If 5 people are randomly selected, what is the probability that at least one of them has been vaccinated?

Answer: P (x ≥ 1) = 0.997

Step-by-step explanation:

We would assume a binomial distribution for the the people that were sampled. The formula is expressed as

P (x = r) = nCr * p^r * q^ (n - r)

Where

x represent the number of successes.

p represents the probability of success.

q = (1 - r) represents the probability of failure.

n represents the number of trials or sample.

From the information given,

p = 69% = 69/100 = 0.69

q = 1 - p = 1 - 0.69

q = 0.31

n = 5

Therefore,

P (x ≥ 1) = 1 - P (x = 0)

P (x = 0) = 5C0 * 0.69^0 * 0.31^ (5 - 0) = 0.003

P (x ≥ 1) = 1 - 0.003 = 0.997