Medical records show that one out of 10 persons in a certain town has a thyroid deficiency. If 12 persons in this town are randomly chosen and tested, what is the probability that at least one of them will have a thyroid deficiency?
Let be the probability of at least 1 person from 12 having the deficiency.
Let be the probability of nobody from 12 having the deficiency.
We can conclude that
Now we just need
Now. If you have 12 people, and each of them has a 0.1 chance of having the deficiency. Then you can say that 12 people have a 0.9 chance of NOT having the deficiency. So what's the probability that ALL of will NOT have the deficiency? Well we know that if two events have 2 probabilities of occuring, then the probability of both occuring is the product of their probabilities. This works the same, although instead of the product of 2 probabilities, we have the product of 12!. .