Event tree - can I add and mulitply the probabilities like this

Question

If I have an event tree such as the following:

Is the following solution then correct to get to B or to D:

$(0.1 \times 0.4) + (0.1 \times 0.6 \times 0.7) = 0.082$

Or should I only use the first branch of $0.1$ only once as it follows the same line?

Answer 1

Here's how you can answer that question for yourself: recast the problem as though you're starting at the orange dot in the middle and trying to get to either B, C or D. Notice that these are the only possibilities, so the sum of their probabilities should be 1.

If I repeat the calculation you gave, I'd get something like: $$0.4 + 0.6 \cdot 0.3 + 0.6 \cdot 0.7$$ What would happen if I instead used the $0.6$ only once?