S1 probability help

Each weekday Alan drives to work. On his journey, he goes over a level crossing. Sometimes he has to wait at the level crossing for a train to pass.


• W is the event that Alan has to wait at the level crossing.
• L is the event that Alan is late for work.


You are given that P(L│W) = 0.4. P(W) = 0.07. P(L or W) = 0.08.


(i) Calculate P(L and W). I have calculated this as 0.4 x 0.07 = 0.028
(ii) Draw a Venn diagram, showing the events L and W. Fill in the probability corresponding to each of the
four regions of your diagram. [3]

This is the bit I am confused on. The picture I have attached below is what the markscheme says.

I don't understand how P(L) = 0.01. This is because
P(L or W) = P(L) + P(W) - P(L and W)
Therefore
0.08 = P(L) + 0.07 - 0.028.
Therefore, I have worked out the probability of L to be 0.038.

Any help would be really really appreciated.
Thank you

0.038 is both the intersection part and the P(L n W')
So P(L n W') Must be 0.038-0.028. Which is 0.01
P(L) is both combined as you worked out

So do you not have to use the formula
P(A or B) = P(A) + P(B) - P(A and B)? I am so confused! Why is 0.038 including the intersection?
Thank you so much for your help

Do you realise P(L) is the whole circle including the intersection?
Since you have worked out the intersection in an earlier part and now worked out that P(L) in total is 0.038 (using that formula). The remaining bit is 0.01. From 0.038-0.028...