Probability, bayes theorem

Question

Good day, hi, would like to ask a math question as follows:

${P(Y_5 = 0 | Y_2 = 0, Y_3 = 1) = \sum_{Y_1, Y_4, Y_6}P(Y_5 = 0, Y_1, Y_4, Y_6| Y_2 = 0, Y_3 = 1)}$

Applying ${P(A|B) = \cfrac{P(A,B)}{P(B)}}$

${\cfrac{= \sum_{Y_1, Y_4, Y_6}P(Y_5 = 0, Y_1, Y_4, Y_6, Y_2 = 0, Y_3 = 1)}{?}}$

What's the denominator?

Please, help out, deadline is around the corner T____T

Answer 1

The denominator is just $P(Y_2=0,Y_3=1)$ since this is the part you are conditioning on. The $A$ in your equation is the event $[Y_5=0,Y_1,Y_4,Y_6]$ and your $B$ is: $[Y_2=0,Y_3=1]$. It is the same for each summand, does this make sense?