I having problem starting this. If 18% of all Americans are underweight, find the probability that if 3 Americans are selected at random, all will be underweight.
That means that the if you select a random American, the chances are 18/100 that they will be underweight. Then, if you select a second random American, the chances are 18/100 that they will be underweight. And likewise, the third, 18/100.
So the chance of ALL 3 being underweight is 18/100 * 18/100 * 18/100.
This is NOT the same as if you had 100 Americans, and 18 of them were underweight.
Yes, the first person would have an 18/100 chance of being underweight, but for the second person there would be a 17/99 chance, and for the third, a 16/98 chance.
The difference here, is that the people chosen are not independent of one another. Removing two underweight people clearly reduces the number of underweight people in the sample, so there's less of a chance the third person will be underweight.
(IF there were replacement, then yes, it would be the same problem...)