More probability confusion

7. (a) Given that P(A) = a and P(B) = b express P(A ∪B) in terms of a and b when (i) A and B are mutually exclusive, (ii) A and B are independent.(2) Two events R and Q are such that P(R ∩Q ҁ) = 0.15, P(Q) = 0.35 and P(R|Q) = 0.1 Find the value of (b) P(R ∪Q),(1) (c) P(R ∩Q),(2) (d) P(R).

With question B I'm getting really confused even though i got the coorect answer. This is as I figured it out by using a venn diagram but when I tried to figure it out via equations I was doing nearly a page work without any correct answer. I want to know if you are just meant to realise that you add the two probabilities given it is only one mark or if there is a simpler way to work it out via equations?

Thanks

By "question B", I presume you mean "Find the value of (b) P(R or Q)". Let me know if that's not what you meant.

P(R or Q) = P(R) + P(Q) - P(R and Q) by the inclusion-exclusion principle (look it up if you haven't heard of it)
then just solve.

Sorry when I was writing this I quoted the number of the wrong question. I actually meant the very last question
'(c) Given that Bill is late, find the probability that he did not travel on foot'

There's nothing about Bill in your initial post: it just talks about events A and B and Q and R.??

Yes you were completely right the first time, sorry it's been a long day for me.
How can you us the principle for a one mark question though? As it requres you figuring out p(R) and P(RnQ). But if you visualise it as a venn diagram you can simply add p(RnQ' and P(Q). This I only figured out when drawing it and could not figure out mathematically.

If a Venn Diagram works for you, do that. It is mathematical and just as valid/rigorous as any other approach!

The thing is I hate venn diagrams and I find myself getting confused quite a lot!