Probability of One Adult Winner in Random Lucky Draw: Homework Solution

[icystrike]

Homework Statement

The question goes like this:
15 men , 10 ladies , 8 girls and boys took part in a lucky draw , A winner was picked at random, after which another winner was picked from the remaining people.

Find the probability that among the two winners , only one of the is an adult.

I understand already! thanks for the PM

Homework Equations

The Attempt at a Solution

I was trying to let An be the nth adult and Cn be the nth Children

and my answer is A1C2+C1C2 or C1A2+C1C2
whereby my answer will be 25/40*15/39+15/40*15/39 or 15/40*25/39+15/40*15/39
however i am wrong..

 

[Office_Shredder]

You seem to be under the false impression that there are 40 people here

 

[futurebird]

Are there 8 girls and 8 boys = 16 kids or 8 kids, both girls and boys?

 

[HallsofIvy]

Are there 8 girls and 8 boys = 16 kids or 8 kids, both girls and boys?

The problem said " 8 girls and boys", NOT "8 girls and 8 boys". There are 25 adults and 8 "non" adults. (Even if you assumed 8 girls and 8 boys, that would be a total of 25+ 16= 41, not 40.)

You say in your first post, "my answer is A1C2+C1C2 or C1A2+C1C2
whereby my answer will be 25/40*15/39+15/40*15/39 or 15/40*25/39+15/40*15/39
however i am wrong.."

Without giving any idea HOW you got that answer.

What is the probability that the first person chosen is NOT an adult? Given that, what is the probability that the second person chosen IS an adult?

What is the probability that the first person chosen IS an adult? Given that, what is the probability that the second person chosen is NOT an adult?

So what is the probability that exactly one of the people chosen is an adult?