The numbers I wrote are from the event tree and given in the problem, in summary I get the below two probabilities of a flashover fire
(0.7 x 10⁻⁶ x 10,000) + 0.4 + 0.5 + 0.8
= (0.007) + 1.7
= 1.707%
And
(0.7 x 10⁻⁶ x 10,000) + 0.6 + 0.1 + 0.8
= 0.007 + 1.5
= 1.507%
I asked you to state details, but in particular, what your three lines in the original work gave probabilities for, not just where the individual numbers came from. "This is the probability of this, that is the probability of that, their product is the probability of this, ..." Stating the meaning of each number, in words, is very important in getting things right; far too many students imagine that math means only writing symbols, when that is far from true.
But why are you now
adding, when I told you before that what you did (
multiplying) looked good? What
reason do you have for adding? You do know, I hope, that "and" basically means multiplication, while "or" means addition (with some caveats).
Once you get these right, think about what the two numbers MEAN. They will be the probabilities of a flash fire happening in two different, mutually exclusive, ways: it can happen either this way,
or that way. How do you combine those to get a single probability of it happening?