probability Question Gcse higher

Stuck on this probability question.

Fiza has 10 coins in a bag. There are three £1 coins and seven 50Pence coins. Fiza takes at random, 3 coins from the bag. Work out the probability that she takes exactly £2.50


I know the answer, its 7/40, because I have the answer on the back of the sheet. But I drew a tree diagram and I got a completely different answer....

I know how to do simple tree diagrams but this one is harder, as she takes a coin three times. So, do you have to eliminate one coin as you go down the tree.. and is there three different sections of the tree?
I know you can work this out without a tree diagram, but I want to know how to work it out with a tree diagram.

Yes, the tree you've described sounds good. Could you show a picture of your tree?

I actually just re-did the whole tree and I got 7/40

I always confuse myself

I've actually done this question when revising. It is conditional probability as she doesn't put the coins back.


So the first coin she gets has a probability of 3/10 being £1 and 7/10 being 50p.


For the next branches, it is out of nine as you only have nine coins left.
If you got £1 then it is 2/9 for £1 and 7/9 for 50p.
If you got 50p then it is 3/9 for the one pound coin and 6/9 for 50p.


For the next branches it is out of 8.
If you got £1 then £1, it is 1/8 for £1 as 2 of the £1 coins are already gone and 7/8 for getting 50pas you haven't gotten any 50p so far.
If you got £1 then 50p it is 2/8 for £1 and 6/8 for 50p.
If you got 50p then £1 it is the same as the one above.
If you got 50p twice, it is 3/8 for £1 and 5/8 for 50p.


Then you multiply along the branches for the ones that add up to £2.50 and add the results together
E.g. for £1 then 50p then £1 it is 3/10 X 7/9 X 2/8

Hope this helps!

I've been looking for a decent explanation for this question for ages - thank you