i was doing these questions for probability and stats and i was wondering why the answers using two different methods dont match.

i'll illustrate with examples

Tree Diagrams (with worked solutions & videos)

in the last two questions they use the outcome approach but if i attempt them using the probabilities of the branches i get the same answers.

here's another question that i shortened just to illustrate

Bag A contains 10 marbles of which 2 are read and 8 are black. Bag B contains 12 marbles of which 4 are red and 8 are black. A marble is drawn at random from each bag. Find the probability that both are red.

for the above question using the outcome approach when the diagram is limited to 2 draws only.. i.e is a total of 4 outcomes.. my answer is 0.25

but if i used the probabilities listed on the tree diagram my answer would be $\displaystyle 2/10 * 4/12 = 1/15$

and these so dont match.

so um.. what am i missing. could someone clarify the situation.

is it because all the numbers or objects are not used here?