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Is my understanding of MIS algorithm true?

I first generate a random number $x\in U(0,1)$ and $w_1=\frac{p_1(direct)}{p_1(direct)+p_2(hemisphere)}$, and then if $x < w_1$ generate the sample directly from the light source, otherwise generate the sample randomly on the unit hemisphere around the hit point.

And what should I do if the randomly generated samples on the hemisphere hit the light source?

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