i should start by saying i am a mature student (embarrassed!!) and it isn't strictly speaking homework but i am using the aqa website to work through past papers as i am self taught. I am struggling with a probability question and i find that using probability trees helps me. Well, the question is:

You have 100 people divided into 14 male managers and 26 male teachers, 8 female managers and 52 female teachers. What is the probability that you will select a male teacher and any female.

On my "tree" i have put the probability of males / females is 2/5 and 3/5 respectively.

I have then on my branch off the "males" i have divided males into 7/20 probability for manager and 13/20 probability for teacher. On my branch off the "females" i have divided females into 2/15 managers and 13/15 teachers.

I worked out then that probability of male teacher = 2/5 x 13/20 and any female = 3/5 x 2/15 plus 3/5 x 13/15

needless to say my answer is wrong (aqa provide mark sheets). Please help!