help with the math part of this - please

[Tasmin]

Hi there, I have created the event tree, but need help is part b) which is the maths part - my scribbles are just my lame half attempt.

Thank you kindly

 

[Dr.Peterson]

Hi there, I have created the event tree, but need help is part b) which is the maths part - my scribbles are just my lame half attempt.

I think the problem is poorly stated. It is a list of conditional probabilities, but seems to leave you to infer the conditions. For instance, I suppose that "extinguished by occupants" is conditioned on being unoccupied; but does "not growing to flashover" assume it is not extinguished.

On the assumption that you understand all that background, can you show us your tree so we can check your work using it? Also, make sure we can tell what the work means; some words help.

 

[Tasmin]

Thank you for replying, here is the event tree as I see it anyway. So there are two different scenarios that lead to the flashover fire (according to my answer)

 

[Dr.Peterson]

Then your work looks good; do you see that you just need to add the two disjoint probabilities you found?

 

[Tasmin]

How do you mean? Like this:
.4 + .5 + .8 = 1.7%
and
.6 + .1 + .8 = 1.5%

Or are the amounts x not +?

Also, I don't understand how to calculate the first part about the 10,000 warehouse with that formula?

 

[Tasmin]

Sorry, or do you mean .8 + .8 = 1.6%

Surely the fire initiation comes into it too though?

 

[Dr.Peterson]

How do you mean? Like this:
.4 + .5 + .8 = 1.7%
and
.6 + .1 + .8 = 1.5%

Or are the amounts x not +?

Also, I don't understand how to calculate the first part about the 10,000 warehouse with that formula?

Sorry, or do you mean .8 + .8 = 1.6%

Surely the fire initiation comes into it too though?

I didn't say that anything you wrote was wrong, such as that the multiplications should be changed to additions; I said your results need to be combined. What does each line you wrote give the probability of?

Your work was



I was assuming that you had some idea what those numbers mean, so that you would understand what I meant by "the two disjoint probabilities you found". But I did miss the bit about fire initiation, so you're right that there's more than one step missing.

Please tell me what the numbers you wrote mean, and then think about how they can be combined to give an answer. Your tree seems very clear about that.

 

[Tasmin]

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%

 

[Dr.Peterson]

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?