In a large population, 57 % of the people have been vaccinated. If 3 people are randomly selected, what is the probability that AT LEAST ONE of them has been vaccinated?

0.92

Step-by-step explanation:

Given

of Population is vaccinated

So, Probability of a person being vaccinated is

and simultaneously , probability of not vaccinated is

Now, Probability that atleast one of them has been vaccinated is given by

The probability that AT LEAST ONE of them has been vaccinated

P( X ≥1)  = 0.920493

Step-by-step explanation:

Step(i):-

Given  57 % of the people have been vaccinated

p = 57% =0.57

q = 1-p =1-0.57 = 0.43

n = 3

Step(ii):-

The probability that AT LEAST ONE of them has been vaccinated

P( X ≥1) = P( x =1) + P(x =2)+P(x=3)            

               =  0.316179 + 0.419121 +0.185193

            = 0.920493

Final -

The probability that AT LEAST ONE of them has been vaccinated

P( X ≥1)  = 0.920493

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