Let XXX and YYY be independent events with P(X)=pP(X) = pP(X)=p and P(Y)=qP(Y) = qP(Y)=q, where 0<p,q<10 < p, q < 10<p,q<1. If P(X∣X∪Y)=23P(X | X \cup Y) = \frac{2}{3}P(X∣X∪Y)=32 and P(Y∣X∪Y)=34P(Y | X \cup Y) = \frac{3}{4}P(Y∣X∪Y)=43, what is ppp?
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