Chance of x = \(\frac{1}{2}\)
Change of Y = \(\frac{2}{3}\)
Chance of Z = \(\frac{1}{4}\)
Chance of Y and Z only occurring
= Pr (Y ∩ Z ∩ X^c)
where X^c = 1 - Pr(X)
1 = \(\frac{1}{2}\) = 1\(\frac{1}{2}\)
= Pr(Y) x Pr(Z) x Pr(X^c)
= \(\frac{2}{3}\) x \(\frac{1}{4}\) x \(\frac{1}{2}\)
= \(\frac{1}{12}\)