Probability of Thyroid Deficiency in Randomly Chosen Group of 12 Persons

[jeevesgarcia]

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 atleast one of them will have a thyroid deficiency.

I know atleast 1 means 1 or 2 or 3 or 4 and so on up to 12. So we just sum all the terms once we get them.

But i am a bit confused on what to do.

Should it be .10( 12!/1!11! + 12!/2!10! + ... + 12!/10!2! + 12!/11!1! + 12!/12!)?

I do not think that is right. can someone explain to me what to do.

The correct answer is .7176

 

[awkward]

There is more than one way to approach this problem, but I think the easiest way is to observe that the probability that at least one person has the disease is 1 minus the probability that none of the 12 have the disease.