How Does Shooter Accuracy Affect Probability of Hitting a Target?

[haruspex]

Looks right to me.
So now, what about P(H;Φ)? Hint: there's an easier way than using p(x).

 

[zeeshahmad]

is it 1 when, theta is greater than Phi?

 

[Simon Bridge]

is it 1 when, theta is greater than Phi?

... when the target area is bigger than the spread of the bullets? Well... yes. That would be part of the answer.

You are thinking along the right lines though...
How about when $\theta < \Phi$?
How would you determine the probability that $\phi$ is inside a certain angle?