Forty 17- and 18-year old students are the only people present at a party.
Male 17 yr olds: 9
Male 18 yr olds: 13
Female 17 yr olds: 7
Female 18 yr olds: 11
In the Grand Draw, each of the forty students has an equal chance of winning one of two prizes. The first prize is a gift token. The second prize is a box of chocolates. No student may win more than one prize. Find the probability that the box of chocolates will be won by a 17 year old, given that the gift token is won by a 17 year old male student.
I tried using the formula P(A and B) / P(B): Here's one attempt: [ (9/40) * (15/39) ]/ 16/40
I did a few other tries, trying different logic, but the answer should be 0.467. I'm very confused.
You can just skip to the second draw after the first has been won by a 17-year old male (so only 8 are left, and 15 17-year olds in total).
The chance of a 17 year old winning in this situation is just $\frac{15}{39}$ and not the answer in your text. That one also mystifies me.
In your attempt the right numbers are $P(B)=\frac{9}{40}$ and $P(A \text{ and} B) = \frac{9}{40}\frac{15}{39}$ and would have given the same.