Probability question

irishdude11

In a class, there are 15 boys and 10 girls. Three students are selected at random. The probability that 1 girl and 2 boys are selected, is -


The correct answer is 21/46
The sample space is 25 choose 3 = 2300

The events are 10 choose 1 multiplied by 15 choose 2 = 1050


1050/2300 = 21/46






What I want to know is why the following doesn't give the same answer -
Pick a girl first, that is 10/25.
Next pick a boy, that is 15/24.
Pick another boy, that is 14/23.


Multiply these probabilities together and you get 7/46.


Anyone know why the 2nd method doesn't work?

MathsManiac

It's because, in your second solution, you've worked out the probability that if you pick three people in a particular order, you end up getting "girl, boy, boy" in that order.

If you also work out the probability of getting "boy, girl, boy", and also "boy, boy, girl", and add these three together, you'll get the same answer as the frst method. (All three are equally likely, so it's just three times 7/46.)