Question

in a large population, 65 % of the people have been vaccinated. if 4 people are randomly selected, what is the probability that at least one of them has been vaccinated?

Answer 1

The probability that at least one of them has been vaccinated is equal to 98.5% if 65% of the people have been vaccinated.

Considering P to be the probability that at least one is vaccinated and q to be the probability that none of the four are vaccinated; the sum of all the probabilities must equal 1; therefore,

P = 1 - q

As 65% of the population is vaccinated, therefore 35% are not vaccinated. Thus any person has a probability of 0.35 of not being vaccinated;

q = 0.35^4 = 0.015

P = 1 - 0.015

P = 0.985

Converting it into percentage;

P = 0.985 × 100 = 98.5%

Therefore the probability that at least one of them has been vaccinated is calculated to be 98.5%

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