Well, I don't know what a probability tree is supposed
to look like, but I'd have expected from the root you'd have a 'split' (two branches) to represent the first outcome (selecting an item from Sinead's pencil case) and then at the end of each
branch you'd have another 'split' (two branches) to represent the second outcome (selecting an item from Joan's pencil case). On each branch you'd write the likelyhood of that event. I'm not sure how easily I can draw that here, but here goes:
Pen / \ Pencil
2/7 / \ 5/7
Pen / \ Pencil Pen / \ Pencil
6/9 / \ 3/9 6/9 / \ 3/9
In probability, an "and" is handled via multiplication. So the end of each 'route' through tree (i.e. at the bottom) can then be labelled with the result of multiplying the two fractions together. So reading left-to-right above, the four outcomes would be 2/7 x 6/9, then 2/7 x 3/9, then 5/7 x 6/9 and finally 5/7 x 3/9.
So the "a pen follower by a pencil" can be read from the result at the bottom of that 'route' and then "at least one pencil" answer can be established by adding the results at the bottom of each 'route' which contains a pencil.
I hope I've explained that sufficiently clearly.