The chances of three independent events X, Y, Z occurring are (frac{1}{2}), (frac{2}{3}), (frac{1}{4}) respectively….

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 ∩ 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})

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