How Does Shooter Accuracy Affect Probability of Hitting a Target?

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is it 1 when, theta is greater than Phi?
 
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?