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.
Best Answer
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.