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?

A.
(frac{1}{8}) 
B.
(frac{1}{24}) 
C.
(frac{1}{12}) 
D.
(frac{1}{4})
Correct Answer: Option C
Explanation
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})