IB AA HL May 2026 P1 TZA Q5

Consider two events, \(A\) and \(B\). It is given that \(P(A\cap B\prime)=\frac{5+x}{24}\), \(P(A\cap B)=\frac{7-x}{12}\) and \(P(A\prime\cap B)=\frac16\), where \(0\leq x\leq7\).

1. Show that \(P(A)=\frac{19-x}{24}\).[3]
2. It is given that \(A\) and \(B\) are independent.
   Find the possible values of \(x\).[6]