Linear Probability Model problem (Binary dependent variables)

y i =a+bD i +u i ,i=1,…,n (LPM equation)

Always thank you for your helps!

I have a question about Linear Probability Model. You can see the model in the above equation. The y i is the dummy dependent variable which is 1 when the voter wants to vote for candidate A and 0 otherwise. Di is also a dummy variable which is 1 when the voter's income level belongs to Top 50% and 0 otherwise. (Assumption: a half of voters' income level belongs to Top 50%, and others' income level belongs to bottom 50%)

How can I calculate the approval ratings of candidate A? (Of course, it would be probability ie, Pr(yi =1) )

After several tries, I got an answer and I want you to see this: I found that Pr(yi =1|Di=1) = a + bDi , and Pr(yi =1) is sum of Pr(yi =1|Di=1) and Pr(yi =1|Di=0) so I made a formula that Pr(yi = 1) = 1/2 * (a+bDi) + 1/2 * a

is this a correct calculation?
I'll wait for your valuable comments.