Help me make a combined NFA for this languag

[zeion]

Homework Statement

Give an NFA and RE for each of the following languages.

L1 = {s \in {a, b, d}* : s contains exactly one occurrence of the substring "dab" and no occurrence of the substring "bad"}

Homework Equations

The Attempt at a Solution

I made two separate NFAs for each condition, then tried to combine them:Do they look right?
How can I simplify the combined one so that I can make a RE expression out of it?
I'm not sure how to make a "trap" state because the accepting states all have different paths to dead states?

Any help appreciated, thanks.
Thanks.

 

[zeion]

No one knows how to make DFA's?