SOLUTION: In a large population, 59 % 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?

Question 666108: In a large population, 59 % 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 by swincher4391(1107) (Show Source): You can put this solution on YOUR website!
We never like "at least one" in probability theory. Always be thinking complement with it. Because the complement of at least one is NONE.
Using our binomial theorem, we want to choose 0 out of the 4.
(4 choose 0) * (.59)^0 * (1-.59)^4 = .0283
Now remember, this is the probability for none, so we need to take turn the complement back into our original.
So the P[at least one] = 1-P[none] = 1 - .0283 = .9717
Hope this helps!
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