# Probability Question

#### aaron7058

##### New Member
Hello I am reviewing one of my exams for my final and am very confused when it comes to this question;

The probability that at least one of the two chosen patients are less than 35 years old?

Given: the sample size is 100. 43/100 of the patients are less than 35 and they are drawn at random (one at a time) without replacement. Any help is appreciated!

Edit: When i previously tried this I obtained the incorrect answer of .8643 and am unsure of how but I am assuming the answer does have to be above .43.

#### Dason

##### Ambassador to the humans
Note that P(At least one is younger than 35) = 1 - P(NOT at least one is younger than 35) = 1 - P(Both are at least 35 years old) = 1 - P(First person chosen is at least 35 and second person chosen is at least 35)

Note that P(First person chosen is at least 35 and second person chosen is at least 35) = P(first person chosen is at least 35) * P(second person chosen is at least 35 | first person chosen is at least 35).

#### aaron7058

##### New Member
So given P(At least one is younger than 35) = 1-P(First person chosen is at least 35 and second person chosen is at least 35) I would form the equation 1-.43*(42/99) = .8175. Am I on the right path?

#### Dason

##### Ambassador to the humans
Note that .43 is the probability of being younger than 35 so you might want to reevaluate your last post.

#### aaron7058

##### New Member
So I would assume the first was not younger than 35 and replace the (42/99) in my last equation with .43?

#### Dason

##### Ambassador to the humans
No - I'm saying that if the probability of being younger than 35 is .43 that the probability of being at least 35 years old is 1-.43

#### aaron7058

##### New Member
ahhh I see, I misread that section! I understand now!

So say 4 patients were selected rather 2 without replacement. If I still wanted the probability that one will be less than 35 how would this differ?