The chances of three independent events X, Y, Z occurring are 12 1 2 , 23 2 3 , 14 1 4 respectively. What are the chances of Y and Z only occurring?

The chances of three independent events X, Y, Z occurring are $\frac{1}{2}$, $\frac{2}{3}$, $\frac{1}{4}$ respectively. What are the chances of Y and Z only occurring?

Answer Details

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 ? Xc)
where Xc = 1 - Pr(X)
1 = $\frac{1}{2}$ = 1$\frac{1}{2}$
= Pr(Y) x Pr(Z) x Pr(Xc)
= $\frac{2}{3}$ x $\frac{1}{4}$ x $\frac{1}{2}$
= $\frac{1}{12}$