in a large population, 66% 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? give your answer as a decimal to 4 places.

There are only two conceivable outcomes for each individual. They are either immunized or they are not. A person's likelihood of receiving a vaccination is unrelated to anyone else. Therefore, to answer this query, we employ the binomial probability distribution.

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

P( X = x ) = Cₙ,ₓ × pˣ × ( 1 - p )ⁿ ⁻ ˣ

In which Cₙ,ₓ is the number of different combinations of x objects from a set of n elements, given by the following formula.

Cₙ,ₓ = n! / x!( n - x )! and p is the probability of X happening.

Now, 66% of the people have been vaccinated.

Therefore, p = 0.66

If 4 people are randomly selected.

Then the probability that at least one of them has been vaccinated will be:

P( X ≥ 1 ) when n = 4

So,

P( X ≥ 1 ) = 1 - P( X = 0 )

Now,

P( X = x ) = Cₙ,ₓ × pˣ × ( 1 - p )ⁿ ⁻ ˣ

P( X = 0 ) = C₄,₀ · ( 0.66 )⁰ · ( 1 - 0.66 )⁴

P( X = 0 ) = 0.01336336

P( X ≥ 1 ) = 1 - P( X = 0 ) = 1 - 0.01336336 = 0.98663664

0.9866 probability that at least one of them has been vaccinated.

Learn more about probability here:

brainly.com/question/13604758

#SPJ4